ji&Binnn 


ahr  0.  R  Bill  Etbrarsj 


iN'nrtli  itarolma   t*tatr  llninprmlij 


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THE 


PRACTICAL  DRAUGHTSMAN'S 

BOOK   OF  INDUSTRIAL   DESIGN, 

AND 

MACHINIST'S  AND  ENGINEER'S  DRAWING  COMPANION: 

FORMING  A  COMPLETE  COURSE  OF 

IPttjnmital,  (feghiecring,  mtfr  ^rtjjiicctaral  gralrag. 

TRANSLATED  FROM  THE  FRENCH  OF 

M.  ARMENGAUD,  THE  ELDER, 

PROFESSOR  OF  DESIGN  IN  THE  CONSERVATOIRE   OF  ARTS  AND  INDUSTRY,  PARIS, 
AND 

MM.  ARMENGAUD,  THE  YOUNGER,  AND  AMOUROUX, 

CIVIL    ENGINEERS. 

REWRITTEN  AND  ARRANGED,  WITH  ADDITIONAL  MATTER  AND  PLATES,  SELECTIONS  FROM  AND  EXAMPLES  OF 
THE  MOST  USEFUL  AND  GENERALLY  EMPLOYED  MECHANISM  CF  THE  DAY. 

BY 

WILLIAM    JOHNSON,   Assoc.  Inst.,  C.E  , 

EDITOR  OF  "THE  PRACTICAL  MECHANIC'S  JOURNAL." 


PRILADELPniA: 

HENRY      CAREY      B  A  I  R  D, 

INDUSTRIAL    PUBLISHER, 

No.    406    "WALNUT    STREET. 

1865. 


PREFACE. 


Industrial  Design  is  destined  to  become  a  universal  language  ;  for  in  our  material  age  of  rapid  transition 
from  abstract,  to  applied,  Science — in  the  midst  of  our  extraordinary  tendency  towards  the  perfection  of  the 
means  of  conversion,  or  manufacturing  production — it  must  soon  pass  current  in  every  land.  It  is,  indeed, 
the  medium  between  thought  and  Execution  ;  by  it  alone  can  the  genius  of  Conception  convey  its  meaning  to 
the  skill  which  executes — or  suggestive  ideas  become  living,  practical  realities.  It  is  emphatically  the 
exponent  of  the  projected  works  of  the  Practical  Engineer,  the  Manufacturer,  and  the  Builder  ;  and  by  its 
aid  only,  is  the  Inventor  enabled  to  express  his  views  before  he  attempts  to  realise  them. 

Boyle  has  remarked,  in  his  early  times,  that  the  excellence  of  manufactures,  and  the  facility  of  labour, 
would  be  much  promoted,  if  the  various  expedients  and  contrivances  which  lie  concealed  in  private  hands, 
were,  by  reciprocal  communications,  made  generally  known  ;  for  there  are  few  operations  that  are  not 
performed  by  one  or  other  with  some  peculiar  advantages,  which,  though  singly  of  little  importance,  would, 
by  conjunction  and  concurrence,  open  new  inlets  to  knowledge,  and  give  new  powers  to  diligence  ;  and 
llersehel,  in  our  own  days,  has  told  us  that,  next  to  the  establishment  of  scientific  institutions,  nothing  has 
exercised  so  powerful  an  influence  on  the  progress  of  modern  science,  as  the  publication  of  scientific  periodicals, 
ia  directing  the  course  of  general  observation,  and  holding  conspicuously  forward  models  for  emulative 
imitation.  Yet,  without  the  aid  of  Drawing,  how  can  this  desired  reciprocity  of  information  be  attained  ;  or 
how  would  our  scientific  literature  fulfil  its  purpose,  if  denied  the  benefit  of  the  graphic  labours  of  tin- 
Draughtsman?  Our  verbal  interchanges  would,  in  truth,  be  vague  and  barren  details,  and  our  printed 
knowledge,  misty  and  unconvincing. 

Independently  of  its  utility  as  a  precise  art,  Drawing  really  interests  the  student,  whilst  it  instructs  him. 
It  instils  sound  and  accurate  ideas  into  his  mind,  and  develops  his  intellectual  powers  in  compelling  him  to 
observe — as  if  the  objects  he  delineates  were  really  before  his  eyes.  Besides,  he  always  does  that  the  best, 
which  he  best  understands  ;  and  in  this  respect,  the  art  of  Drawing  operates  as  a  powerful  stimulant  to 
progress,  in  continually  yielding  new  and  varied  results. 

A  chance  sketch — a  rude  combination  of  carelessly  considered  pencillings — the  jotted  memoranda  of  a 
contemplative  brain,  prying  into  the  corners  of  contrivance — often  form  the  nucleus  of  a  splendid  invention. 
An  idea  thus  preserved  at  the  moment  of  its  birth,  may  become  of  incalculable  value,  when  rescued  from  the 
desultory  train  of  fancy,  and  treated  as  the  sober  offspring  of  reason.  In  nice  gradations,  it  receives  the 
refining  touches  of  leisure — becoming,  first,  a  finished  sketch, — then  a  drawing  by  the  practised  hand  so  that 
many  minds  may  find  easy  access  to  it,  for  their  joint  counsellings  to  improvement — until  it  finally  emerges 
from  the  workshop,  as  a  practical  triumph  of  mechanical    invention— an  illustrious  example  of  a  happy 


combination  opp-  men  arc  barely  able  even  to  Mart  th 

r  furnish  that  tr  . 
umortal.      i 
,|  »n  iu  Object  ;  for  it  will  at  least  add  I  I  the  ladder  of  Intelligence, 

and  form  a  few  more  I  '.Vction — 

"Thou  hut  not  W  an  hour  »h*r«>f  ihrr*  u  *  Ml  _ 

A  wniuu  thought  mt  midnight  will  roJeem  th«  livelong  d»y." 

T,  v  necessary  as  the  ordinary  rudiment*  of  ]ear- 

,.  in  the  edl  :uent 

iy  intend  I  i;  tor  without  a  know 

Manufactures,  can  be  a 
and  the  routines  of  study  in  all  varicti 
j  the  introduction  of  fas 

The  special  mi--ion  .  .f  the  Practical  Draughtsman's  Book  of  Industrial  Design  may  a:  ered  from 

I  to  furnish  gradually  di  BJOtrical  I ►rawing,  applied  directly 

of  the  Industrial   \  Hag  Linear  Design  pr 

■  >ns  ;  the  Prawn  E  aiag  and  C 

tod  the  study  ..f  parallel  and  • 

f  Mechanics,  Architecture,  Foundry-W 

•ally.  11yd:  I  Mill-Work.     In 

ipilation.  •  ncrally  ot:  toy  foraffc  .fully 

brieal  problem,  a  practical  exampl  i  lieation  has  be- 1 

facili'  -.due. 

The  work  is  comprised  within  nine  divisions,  appropriated  to  the  different  branches  of  Industrial  D 
The  first,  vkieb  •  irticularh 

apple 

•  ident  t"  the  proper  ase  of  I     - 
exampl. -s  of  different  nethoda  of  oonBtrnctiiig  plain  i 
in  ni.  the  ellipse,  the  oral,  the  pai  and  the  roluti 

accura 

lloetratei  the  geometri  station  of 

practicallj  considered.    It  shows  thai 

:  initiation  of  all  tl 

for  the  die  .;ion  of  internal  : 

D  points  OOl  tionnl  colours  and  tin! 

ofol  to  their  nature  ;  famishing,  at  the  rimple  and  ca-v  examples,  which   I 

I  the  pupil,  and  hmniajt—  bjffl  with  the  u-e  of  the  ; 

In  the  foarth  di'. 

.  with  the  '  '."pnicnt,  hi 

appl  Cocke. 

and  cluai  '  lus« 


PREFACE. 


The  fifth  division  is  devoted  to  special  classes  of  curves  relating  to  the  teeth  of  Spur  Wheels,  Screws 
and  Racks,  and  the  details  of  the  construction  of  their  patterns.  The  latter  branch  is  of  peculiar  importance 
here,  inasmuch  as  it  has  not  been  fully  treated  of  in  any  existing  work,  whilst  it  is  of  the  highest  value  to  the 
pattern  maker,  who  ought  to  be  acquainted  with  the  most  workmanlike  plan  of  cutting  his  wood,  and 
effecting  the  necessary  junctions,  as  well  as  the  general  course  to  take  in  executing  his  pattern,  for  facilitating 
the  moulding  process. 

The  sixth  division  is,  in  effect,  a  continuation  of  the  fifth.  It  comprises  the  theory  and  practice  of 
drawing  Bevil.  Conical,  or  Angular  Wheels,  with  details  of  the  construction  of  the  wood  patterns,  and 
notices  of  peculiar  forms  of  sonic  gearing,  as  well  as  the  eccentrics  employed  in  mechanical  construction. 

The  seventh  division  comprises  the  studies  of  the  shading  and  shadows  of  the  principal  solids — Prisms, 
Pyramids,  Cylinders,  and  Spheres,  together  with  their  applications  to  mechanical  and  architectural  details, 
as  screws,  spur  and  bevil  wheels,  coppers  and  furnaces,  columns  and  entablatures.  These  studies  naturally 
lead  to  that  of  colours — single,  as  those  of  China  Ink  or  Sepia,  or  varied  ;  also  of  graduated  shades  produced 
by  successive  flat  tints,  according  to  one  method,  or  by  the  softening  manipulation  of  the  brush,  according 
to  another. 

The  pupil  may  now  undertake  designs  of  greater  complexity,  leading  him  in  the  eighth  division  to  various 
figures  representing  combined  or  general  elevations,  as  well  as  sections  and  details  of  various  complete 
machines,  to  which  are  added  some  geometrical  drawings,  explanatory  of  the  action  of  the  moving  parts 
of  machinery. 

The  ninth  completes  the  study  of  Industrial  Design,  with  oblique  projections  and  parallels,  and  exact 
perspective.  In  the  study  of  exact  perspective,  special  applications  of  its  rules  are  made  to  architecture  and 
machinery  by  the  aid  of  a  perspective  elevation  of  a  corn  mill  supported  on  columns,  and  fitted  up  with  all 
the  necessary  gearing.  A  series  of  Plates,  marked  A,  B,  <fec,  are  also  interspersed  throughout  the  work,  as 
examples  of  finished  drawings  of  machinery.  The  Letterpress  relating  to  these  Plates,  together  with  an 
illustrated  chapter  on  Drawing  Instruments,  will  form  an  appropriate  Appendix  to  the  Volume.  The  general 
explanatory  text  embraces  not  only  a  description  of  the  objects  and  their  movements,  but  also  tables  and 
practical  rules,  more  particularly  those  relating  to  the  dimensions  of  the  principal  details  of  machinery,  as 
facilitating  actual  construction. 

Such  is  the  scope,  and  such  are  the  objects,  of  the  Practical  Draughtsman's  Book  of  Industrial  Design. 

Such  is  the  course  now  submitted  to  the  consideration  of  all  who  are  in  the  slightest  degree  connected 
with  the  Constructive  Arts.  It  aims  at  the  dissemination  of  those  fundamental  teachings  which  are  so 
essentially  necessary  at  every  stage  in  the  application  of  the  forces  lent  to  us  by  Nature  for  the  conversion 
of  her  materials.  For  ;1  man  can  only  act  upon  Nature,  and  appropriate  her  forces  to  his  use,  by  compreheuding 
her  laws,  and  knowing  those  forces  in  relative  value  and  measure."  All  art  is  the  true  application  of 
knowledge  to  a  practical  end.  We  have  outlived  the  times  of  random  construction,  and  the  mere  heaping 
together  of  natural  substances.  We  must  now  design  carefully  and  delineate  accurately  before  we  proceed 
to  execute — and  the  quick  pencil  of  the  ready  draughtsman  is  a  proud  possession  for  our  purpose.  Let  the 
youthful  student  think  on  this  ;  and  whether  in  the  workshop  of  the  Engineer,  the  studio  of  the  Architect, 
or  the  factory  of  the  Manufacturer,  let  him  remember  that,  to  spare  the  blighting  of  his  fondest  hopes,  and 
the  marring  of  his  fairest  prospects — to  achieve,  indeed,  his  higher  aspirations,  and  verify  his  loftier  thoughts, 
which  point  to  eminence — he  must  give  his  days  and  nights,  his  business  and  his  leisure,  to  the  study  of 

iJnbustrial   DtBtgn. 


ABBREVIATIONS  AND  CONVENTIONAL  SIGNS. 


In  order  to  simplifv  the  language  or  expression  of  arithmetical  ami  geometrical  operations,  the  following  conventional 
•ign»  are  used  : — 

The  »ign  +  signifies  plus  or  more,  and  is  pl.t  « o  or  more  terms  to  indicate  additior. 

Eia v  4  +  3,  is  4  plus  3,  that  is,  4  added  to  3,  or  7. 

fie*  minus  or  Itss,  and  indicates  su! 'traction. 
Ex. :  4  —  3,  is  4  minus  3,  that  is,  3  taken  from  4,  or  1. 

The  sign  X  signifies  multiplied  by,  and,  placed  between  two  terms  indicates  mullip) 

5  x  3,  is  5  multiplied  bj  8,  or  15. 
quantities  are  expressed  i  mippi  eased     Hun  we  writ.-,  indifferently — 

a  x  b,  or  ab. 
The  sign  :  or  (as  it  is  more  commonly  used  i    -  Uwidtd  by,  and,  placed  between  two  qua  it. -*  division. 


Bx 


12 
12  :  4,  or  12  -J-  4,  or  — ,  I  by  4. 


The  si--  '*  or  aawaJ  to,  and  b  -ions  t.>  indi  tality. 

0  +  2  =  8,  meaning,  tli.it  0  ]  i  to  8. 

•  >n  of  these  eigne,  :  ::  I  indicatea  geometrical  proportion. 

: :  i  :  ,;,  nn  an  ng,  thai  8  a  to  8  .■«  4  is  to  0. 
The  sign  V—  indicates  the  extraction  of  a  root;  as, 

Vi)-^.  meaning,  thai  the  equate  root  of  9  is  equal  to  3. 
The  ml  rpoaition  of  a  Tin 

■J/J7  =  3,  expresses  that  the  cube  root  of  27  ii  equal  to  3. 
The  signs  ^  and  7  indica'-  i  and  pnagfcr  than. 

3  /  4,  =  3  mii.iINt  than  1 ,  ai  y,  4  7  8,  =  4  greater  than  3. 

Fig.  signifies  figure;  and  pL, 


10  Millimetre* 

= 

= 

10  DetJraetm 

= 

1    M.T, 

10  Metra 

= 

1  I  ►'  ■  am»'tr« 

= 

1  !!••.• 

= 

lo  Kumwtm 

■ 

-.rnrtr* 

FRENCH  AND  ENGLISH  LINEAR  MEASURES  n»M!'\l:i.I>. 


•0894  Inolic*. 
•S9S7       " 
**•»»*  1       " 

rarda 

■• 

-ng*. 
:  I     6J|:-  ' 
:     6213>' 


m\ 

•- 
thnetm, 

II     In.  he. 

= 

= 

• 

= 

1  Y*rJ 

= 

'.-in 

1  .rJ« 

= 

1  Pol*  or 

= 

= 

1  Furlong 

- 

• 

rlong*  ) 

i  aide      i 

= 

= 

1  ■  !"  I; 

CONTENTS. 


Preface,       - 

Abbreviations  and  Conventional  signs, 


Tiar. 

iii 


CHAPTER   I. 

LINEAR  DRAWING,      - 
Definitions  and  Problems  :  Plate  I. 
Lines  and  surfaces,    - 

Applications. 

Designs  for  inlaid  pavements,  ceilings,  and  balconies 

Plate  II.,  - 

Sweeps,  sections,  and  mouldings  :  Plate  III., 
Elementary  Gothic  forms  and  rosettes :  Plate  IV, 
Ovals,  Ellipses,  Parabolas,  and  Volutes  :  Plate  V, 

Rules  and  Practical  Data. 
Lines  and  surfaces,  - 


-    ib. 


-  II 

-  13 
.     14 

,     15 

-  19 


CHAPTER    II. 

THE  STUDY  OF  PROJECTIONS,       -           -           -  22 

Elementary  Principles  :  Plate  VI. 

Projections  of  a  poiDt,          -                        -           -  ib. 

Projections  of  a  straight  line,           -            -            -  23 

Projections  of  a  plane  surface,         -            -            -  tb. 

Op  Prisms  and  Other  Solids  :  Plate  VII.,     -            -  24 

Projections  of  a  cube :  Fig.  lh,         -            -            -  ib. 

Projections  of  a  right  square-based  prism,  or  rectan- 
gular parallelopipcd :  Fig.  [§,                     -            -  25 

Projections  of  a  quadrangular  pyramid  ;  Fig.  ©,     -  ib. 

Projections  of  a  right  prism,  partially  hollowed,  as 

Fig.®, ib. 

Projections  of  a  right  cylinder  :  Fig.  H,      -            -  ib. 

Projections  of  a  right  cone  :  Fig.  \f,            -            -  ib. 

Projections  of  a  sphere  :  Fig.  (g,                  -            -  26 

Of  shadow  lines,        -            -            -            -            -  ib. 

Projections    of   grooved   or   fluted    cylinders   and 

ratchet-wheels :  Plate  VIII.,       -            -            -  27 

The  elements  of  architecture  :  Plate  IX.,  -            -  28 

Outline  of  the  Tuscan  order,             -            -            -  29 
Rules  and  Practical  Data. 

The  measurement  of  solids,  -            -            -            -  30 


CHAPTER  HT. 

ON    COLORING    SECTIONS,    WITH    APPLICA- 
TIONS. 

Conventional  colors,  -    .       -  -  - 

Composition  or  mixture  of  colors  :  Plate  X., 
Continuation  of  the  Study  of  Projections. 

Use  of  sections — details  of  machinery  :  Plate  XL, 

Simple    applications — spindles,    shafts,    couplings, 
wooden  patterns  :  Plate  XII.,     - 

Method  of  constructing  a  wooden  model  or  pattern 
of  a  coupling,         - 

Elementary  applications — rails  and  chairs  for  rail- 
ways :  Plate  XIII. ,  - 
Rules  and  Practical  Data. 

Strength  of  materials,  - 

Resistance  to  compression  or  crushing  force, 

Tensional  resistance,  - 

Resistance  to  flexure,  - 

Resistance  to  tordon,  - 

Friction  of  surfaces  in  contact,         - 


35 
ib. 


36 


CHAPTER  IV. 

THE  INTERSECTION   AND  DEVELOPMENT  OF 
SURFACES,  WITH  APPLICATIONS,    - 
The  Intersections  of  Cylinders  and  Cones  :  Plate 
XIV. 
Pipes  and  boilers,     - 
Intersection  of  a  cone  with  a  sphere, 
Developments,    ------ 

Development  of  the  cylinder,  - 

Development  of  the  cone,     - 
The    Delineation    and    Development    of    Helices, 
Screws"  and  Serpentines:  Plate  XV. 

Helices,         ------ 

Development  of  the  helix,     -  -  -  - 

Screws,  -  -  -  -  - 

Internal  screws,         - 

Serpentines,  ------ 

Application   of  the   helix — the  construction   of  a 
staircase  :  Plate  XVI.,    -  -  -  - 


-    49 


52 
53 
ib. 

54 
ib. 

55 


The  intersection  of  sarTacca     application*  to   - 
cock.  -    a 

Be  LX«  AID  I'»  . 



f  heat,  .... 

ng  swrtace,  -  -     II 

Atioa  of  the  dxiemsioM  of  bodeta,  -    ib. 

Ihsaensions  of  firegrate,  -61 

;<        • 
Safety-valves, 


CHAPTER   V. 

63 

'.oid.  an.l  epicycloid:  Plates  XVIII. 
and  I 

VIII.      -  -  -    i%. 

»ti  XVIII..       -  -  -     64 

;    described   by  a  circle  rolling 
aboc- 

-  ib. 
Alien  of  a  rack  and  pinion  in  gear :  Fig.  4, 

-  ib. 
Gearing  of  a  worm  with  a  worm-wheel :  Figs.  5  and 

I,  Pun  TOIL, 67 

bbical  ob  Srra  QsaMm :  Pun 

ml  delineation  of  two  (par-wheels  in  gear: 

ib. 

v.ion  of  a  couple  of  wheels  gearing  internal! v  : 

68 

I    »1  delineation  of  a  couple  of  spur-wheels : 

.    69 
T»r  MB  PaT- 

tsess  roa  Toothed  Wuku  :  Flats  X\i.. 
•  .eel  patterns, 

rn  of  the  pinion,  -  -  -  •    ib. 

•  :.e  wooden-toothed  spur-» !  -    71 

-  |0. 
'  vTA. 

Toothed  gearing,      .... 

Angalar  and  circumferential  Telocity  of  wheels,     -     74 
asiuas  of  gear.-  .- 
♦*  of  the  teeth. 

f  the  teeth,    -  -  -  -  -     7« 

.on*  of  the  web,  .  -77 

•er  and  dimensioos  of  the  arms,  -    ib. 

icn  patterns,     - 


CHAPTER    VI. 

.      V  TOOTHXD 


Pi    (TI 


.'.  or  beril  gearinr. 
Design  for  a  pair  of  ben]. wheels  in  gear 

. 

Ct;  *  rf>den  patterns  for  a  pair  of  beril- 

III..    - 
I 

»  beels.  with  involute 

Helical  gear;  14.. 

ComiTixr-  ,  ;.i»T]  kLMoTKYtxra. 


•  a. 


-  o>. 


■   -  i 


The  delineation  of   eccentrics   and   cams:    Flati 

\w 

.  -  ... 

rt-»haped  cam:  Fig.  1.  - 
Car  rn   and    intermittent 

morement :  Fig*  2  and  3,  ... 

Triangular  cam  :  Figs.  4  and  5,        - 
Inrolnte  cam  :  Figs.  6  at  i  7.  -  -  - 

Cam  to  produce  intermittent  and  **i«*imil*r  move- 
ments :  Figs.  6  and  9,        - 
Rcxks  ASP  Fsi 

The  simple  machines,  .... 

Centre  of  gravity,     ..... 
On  estimating  the  power  of  prime  movers,  - 

.lation  for  tbe  brak-  -  .  -    ib. 

The  fall  of  bodies,     -  -  -  -  -    95 

Momentum,  ....  .    ib. 

ral  forces,  -  -  -  -  -    i 


rnAiira  vu. 
KI.KMrNTAP.V  PItIN<  -    96 

Shadows  or  Faisxs,  Ptrakids.  axd  Ctuxdies  :  Flati 
WVl. 

. 
.mi.l.        ..... 

Truncated  pyramid,  -  -  -  -  M 

-  ib. 
w  cast  by  one  cylinder  on  an otb<  r.  -  -  if>. 
m  cast  by  a  cylinder  on  a  pr:-m,         -            -    ib 

low  cast  by  one  prism  on  Mot]    r  .     99 

•v  cast  by  a  prism  on  a  cyhn-i  r.  -  -    ib. 

Pbixctplbs  Pi  HI   \\V1I..  .  .  M0 

rfcee*, ■*. 

-  i7.. 
Ml 

Shading  by  soft. ■:. 

■  x    or    THB     -  '    krt 

XWIII. 

I  caM  upon  the  interior  of  a  cylinder,  -  103 

Shadow  ca--  far  upon  another,  •    ib. 

-       lows  of  cone-  -  •    ib. 

- 

v  cast  upon  the  interior  of  a  hollow  cone,     •  106 

-  ib. 

rus,  -  -  •  ib. 

m  cast    by  a  straight  line  upon  a  tor 

quarter  round,        .....  |n7 

*  s  of  surfaces  of  revolution.    -  -  -  if.. 

Re:  - 

Pumps.  .  .  .  .  .  .  : ' ■- 

',•■■•  AV 

T'«.  -  -  -  -       10. 

r  pump*,   ... 
Tbe  hydrostatic  press,  -  -  -     ib. 

i!  calculations  and  data — discharge  of 
water  throi..  BcM,    -  -  •    ib. 

rm  section  and  fall.  110 
.  -     -       -  -     ib. 

Calculation  of  the  discharge  of  water  through  rect- 
angular orifice*  of  narrow  edge*,  -  -  111 


CONTENTS. 


Calculation  of  the  discharge  of  water  through  over- 
shot outlets,  - 
To  determiue  the  width  of  an  overshot  outlet, 
To  determine  the  depth  of  tho  outlet, 
Outlet  with  a  spout  or  duct,  - 


-  ib. 

-  116 


CHATTER   VIII. 

ArrUCATION    OF    SHADOWS    TO    TOOTHED 
GEAR:  Plate  XXX. 

Spur-wheels  :  Figs.  1  and  2,  -  -  -  -    ib. 

licvil-whccls  :  Figs.  3  aud  4,  -  -  -117 

Application  of  Shadows  to  Screws  :  Plate  XXXI.,  118 
Cylindrical  square-threaded  screw  :  Figs.  1,  2,  2", 

and  3,  -  -  -  -  -    ib. 

Screw  with  several  rectangular  threads:  Fig?.  4  and  .">.     ib. 

Triangular-threaded  screw :  Figs.  6,  6°,  7,  and  8,     -    ib, 

Shndows  upon  a  round-threaded  screw :  Figs.  9  and  10,  119 

Application  of  Shadows  to  a  Boiler  and  its  Furnace  : 

Plate  XXXII. 

Shadow  of  the  sphere  :  Fig.  1,  ...    ib. 

Shadow  cast  upon  a  hollow  sphere  :  Fig.  2,  -  120 

Applications,  .....    ib. 

Shading    in    Black — Shading    in   Colours  :    Plate 

XXXIII., 122 


CIIAMER   IX. 

THE  CUTTING  AND  SHAPING  OF  MASONRY: 

Plate  XXXI V., 

The  Marseilles  arch,  or  arriZre-voussxire :  Figs.  1 
and  2, 
Br/l.ES  and  Practical  Data. 
Hydraulic  motors,     - 

I  udershot  water-wheels,  with  plane  floats   and  a 
circular  channel,   - 

•Width, 

Diameter,      ...... 

Velocity,       ...... 

Number  and  capacity  of  the  buckets, 

Useful  effect  of  the  water-wheel,       ... 

Overshot  water-wheels,        -  ,  ,  . 

Water-wheels,  with  radial  floats,     - 

Water-wheels  with  curved  buckets, 

Turbines,       ...... 

Remarks  oh  Machine  Tools,     -  -  ,  . 


123 
ib. 


ib. 
ib. 
127 
ib. 

ib. 

ib. 
128 
129 
130 

ib. 
131 


CHAPTER  X. 

THE  STUDY  OF  MAOHIN  KEY  AND  SKETCHING. 

Various  applications  and  combinations,          -             -  133 
The  Sketching  of  Machines?  :   Plates  XXXV.  and 

XXXVI., ib. 

Drilling  Machine,          -            -            -            -            -  ib. 

Motive  Machines. 

Water-wheels,          ......  135 

Construction  ami  setting  up  of  water-wheels,           -  ib. 
Delineation  of  water-wheels,            -           -          -136 

Design  for  a  water-wheel,     ....  137 

Sketch  of  a  water-wheel,       -            -            -            -  ib. 

Overshot  Water- Wheels  :  Fig.  12,      ...  ib. 
Delineating,    sketching,    and    designing    overshot 

water-wheels,          .....  138 


Water-Pumps  :  Plate  XXX  VII. 

Geometrical  delineation,        ....  138 
Action  of  the  pomp,  -  ....  139 

Steam  Motors. 

High-pressure     expansive    steam-engine:    Plates 
XXXV  in.,  XX  XIX,  and  XL.,  -  -  -  141 

Action  of  the  engine,  -  -  -  -142 

Parallel  motion,         -  -  -  -  -    ib. 

Details  of  Construction. 

Steam  cylinder,         .....  143 

Piston,  -  -  -  -  -  -    ib. 

Connecting-rod  and  crank,   -  -  -  -    ib. 

Fly-wheel,     -  -  -  -  -  -    ib. 

Feed  pump,    .....  ib. 

Ball  or  rotating  pendulum  governor,  -  144 

Movements  of  the  Distribution  and  Expansion  Valves,    ib. 

Lead  and  lap,  .....  145 

Rules  and  Practical  Data. 

Strum-engines:   low   pressure    condensing    engine 
without  expansion  valve,   ...  -  146 

Diameter  of  piston,    -----  147 

Velocities,     ------  148 

Steam-pipes  and  passages,    ...  -    ib. 

Air-pump  and  condenser,      ....    ib. 

Cold-water  and  feed-pumps,  ...  -  149 

High  pressure  expansive  engines,     ...    2"j. 

Medium  pressure  condensing  and  expansive  steam- 
engine,        ......  151 

Conical  pendulum,  or  centrifugal  governor,  -  153 


CnAFTER   XI. 

OBLIQUE  PROJECTIONS. 

Application  of  rules  to  the  delineation  of  an  oscilla. 
ting  cylinder :  Plate  XLI, 


-  154 


chapter  xii. 
PARALLEL  PERSPECTIVE. 

Principles  aud  applications  :  Plate  XLIL, 


CHArTER    XIII. 

TBUE  PERSPECTIVE. 

Elementary  principles :  Plate  XLIII,        -  -158 

First  problem — the  perspective  of  a  hollow  prism  : 

Pigs.  1  and  2,         -  -  -  -  -    ib. 

Second   problem — the   perspective   of-  a  cylinder: 

3  and  4,  -  -  -  -  159 

Third  problem — the  perspective  of  a  regular  solid, 

when  the  point    of  sight    is   situated   in   a   plane 

passing  through  its  axis,  and  perpendicular  to  the 

plane  of  the  picture  :  Figs.  5  and  G, 
Fourth  problem — the  perspective  of  a  bearing  brass, 

placed  with  its  axis  vertical  :  Figs.  7  and  8, 
Fifth  problem — the  perspective  of  a  stopcock  with 

a  spherical  boss :  Figs.  9  and  10,  - 
Sixth  problem — the  perspective  of  an  object  placed 

in  an]  position  with  regard  to  the  plane  of  the 

picture:  Figs.  11  and  12,  - 
Applications — Sour-mill   driven  bv  belts:   Plates 

Xl.IV.  and  XI.V. 

Description  of  the  mill, 


ICO 


ib. 


-    ib. 


161 


-    ib. 


Representation  of  the  Bill  b 

'  recent  improvement*  la  luar-mill*, 

- 
-ullstone,"     • 

- 

i 


Work  pel  formed  bj  ranon*  machines, 

- 

:     -        - 
:  saw». 


ICO 

a. 


171 

•1. 


cn.wTi  R   i 

MA- 
CUIJi 

i!ance  water- meter.  .  1TJ 

ng  machine,       •  174 

i  vrens  locomotire  engine,  17i* 

aning  machine.  . 

-  i-hiiir  machine  lor  pine*  goods,  183 

•m. 


I    .'•-. 


Eiamj  I't-actmg  manac  engine*. 


rn.MTn  xv. 
I'RAW  I 


1-i 


I  N  D  KX    TO    T  II  K    TA  15  1      - 


- 
. 

'  .ta!  m.  -asur  -  h  millime- 

tres and  English  fcet, 

and  volume*  of  regular  po! 

•0*1  meaaor  I 
(m,  .... 

•nal   ni<  i-up  mint- 
Tuscn:  .... 

\  <-och  ascoluu  supports, 

- 

..n  when 

submitted  to  »  lcn>Uc  strain. 

Diameter*  of  the  joarnali  of  water-wheel  and  other  shafts 

for  heary  work.     -  .  -  -  - 

r*  for  shaft  journals  calcu!  rence  to 

. 

Ratio*  of  irnals  in  !•■-.. 

Piimuu,  temperatures,  w> 

aeas  of  plate*  in  cylindrical  i 

of  ire  »tm-.'|l,ir«,  .... 

IHajMtm  ..l.^'j-iilin,  . 

- 
I' 


6- 

21 
30 

33 


a 


u 
4$ 

I*. 


MM 

Dime:  rms. 

Average  amount  of  mechanical  i 

and  animal*.  -  •  -    W 

•  nndinc  to  various  velocities  of  falling  bodies,    94 

measures  of  capacity.  .  110 

'  water  through  an  orifice  one  mMre  in  width.  Ill 

v  metre  in  width,  1 1 3 

-  115 
1                                                            irinus  kinds  of  turbine*.  131 

i  pressure  of  maehir  Mr*, 

:.s  steam  engine*,  with  the  quantities  of  steam 

-  It" 
I  \  en  out  with  various  degrees  of 

expansion,  by  a  cobic  metre  of  steam,  at  rations  pres- 
sure.        .....  .  150 

engines,  condensing  and 
the  steam 
r  atmosphere*  in  the  coo- 
ing,  and  at  fire  atmospheres  in  the  other  engine' 
m  pressure  condensing  and  expa- 

-  ib. 

..•ns  of  the  arm*,  a:  f  the  balls  of  the 

>l  pendulum,  or  cen'- 
1'  I   and  number  of  pair*  of 

.t-alus,  required  in  £ 

■  16» 


PRACTICAL    DRAUGHTSMAN'S 


BOOK  OF  INDUSTRIAL  DESIGN. 


CHAPTER  I. 
LINEAR  DRAWING. 

In  Drawing,  as  applied  to  Mechanics  and  Architecture,  and  to  tho 
Industrial  Arts  in  general,  it  is  necessary  to  consider  not  only  the 
mere  representation  of  objects,  but  also  the  relative  principles  of 
action  of  their  several  parts. 

The  principles  and  methods  concerned  in  that  division  of  tho 
art  which  is  termed  linear  drawing,  and  which  is  the  foundation  of 
all  drawing,  whether  industrial  or  artistic,  are,  for  the  most  part, 
derived  from  elementary  geometry.  This  branch  of  drawing  has 
for  its  object  the  accurate  delineation  of  surfaces  and  the  con- 
struction of  figures,  obtainable  by  the  studied  combinations  of 
lines;  and,  with  a  view  to  render  it  easier,  and  at  tho  same  timo 
more  attractive  and  intelligible  to  tho  student,  the  present  work 
'i  arranged  to  treat  successively  of  definitions,  principles, 
and  problems,  and  of  tho  various  applications  of  which  these  are 
capable. 

Many  treatises  on  linear  drawing  already  exist,  but  all  these, 
red  apart  from  their  several  objects,  seem  to  fail  in  the  due 

development  of  tho  subject,  and  do  not  manifest  that  general  ad- 
vancement and  increased  precision  in  details  which  are  called  for 
at  tho  present  day.  It  has  therefore  been  deemed  necessan  to 
begin  with  these  rudimentary  exercises,  and  such  exemplifications 
have  been  selected  as,  with  their  varieties,  are  most  frequently 
met  with  in  practice. 

Many  of  the  methods  of  construction  will  be  necessarily  such  as 
are  already  known;  but  they  will  be  limited  to  those  which  are 
absolutely  indispensable  to  the  development  of  the  principles 
and  their  applications. 


DEFINITIONS. 

OF   LltlES   AND   SURFACES. 
PLATE    I. 

In  Geometry,  apace  is  described,  in  the  terms  of  its  threi  dimen- 
sions— length,  oreadth  or  thickness,  and  height  or  depth. 

The  combination  of  two  of  these  dimensions  represents  surface. 

and  one  dimension  takes  the  form  of  a  line. 


Mats. — There  are  several  kinds  of  lines  used  in  drawing— 
straight  or  right  lines,  curved  lines,  and  irregular  or  broken  lines. 

Right  lines  are  vertical,  horizontal,  or  inclined.  Curved  lines  are 
circular,  elliptic,  parabulic,  tSfC. 

Surfaces. — Surfaces,  which  are  always  bounded  by  lines,  aro 
plane,  concave,  or  convex.  A  surface  is  plane  when  a  straight-edge 
is  in  contact  in  every  point,  in  whatever  position  it  is  applied  to  it. 
If  the  surface  is  hollow  so  that  the  straiuht-edge  only  touches  at 
each  extremity,  it  is  called  concave;  and  if  it  swells  out  so  that 
the  straight-edge  only  touches  in  one  point,  it  is  called  convex. 

Vertical  liars. — By  a  vertical  line  is  meant  one  in  the  position 
which  is  assumed  by  a  thread  freely  suspended  from  its  upper  ex- 
tremity, and  having  a  weight  attached  at  the  other;  such  is  the 
line  AB  represented  in  fig.  ^.     This  line  is  always  straight,  and 

the  shortest  that  can  be  drawn  between  its  extreme  points. 

Plumb-line. — -The  instrument  indicated  in  tig.  .A  is  called  a 
plumb-line.    It  is  much  employed  in  building  and  the  erection 

of  machinery,  as  a  guide  to  the  construction  of  vertical  lines  and 
surfaces. 

Horizontal  line. — When  a  liquid  is  at  rest  in  an  open  vessel,  its 

upper  surface  forms  a  horizontal  plane,  and  all  lines  drawn  upon 
such  surface  are  called  horizontal  lines. 

Levels. — It  is  on  this  principle  that  what  arc  called  fluid  levels 
are  constructed.      One  description   of  fluid    level    consists  of  two 

upright  glass  tubes,  connected  by  a  pipe  communicating  with  the 

bottom  of  each.  When  the  instrument  is  partly  tilled  with  water, 
the  water  will  stand  at  the  same  height  in  both  tubes,  and  thereby 
indicate  the  true   level.      Another  torn),  and   more    generally 

used,  denominated  a  spirit  level — spirit  being  usually  employed— 
consists  of  a  glass   tube  (fig.   ©)  enclosed  in  a  metal  case.  ,/, 

d  by  two  supports,  b,  to  a  plate,  c.  The  tube  is  almost 
filled    with    liquid,    and    the   bubble   of  air,  d,   which    remains,  is 

exact]]  in  the  centre  of  the  tube  when  any  surface,  c  d,  os 

Which  the  instrument  is  placed,  is  perfectly  level. 

Masons,  carpenters,  joiners,  and   other  mechanics,  are  in  (he 
habit  of  using  the  instrument  represented   in  t'vj.  Q.  em 
simply  of  a  plumb  line  attached  to  the  point  of  junction  of  the  two 

inclined  side  pieces,  ah.  Ac,  of  equal  length,  and  connected  near 
their  free   ends    by  the   cr.i-s-pi.ee,  An,  which   has  a  mark   at  its 


Tin:  ; 


V.       .  thr  jWumb  lin.  h  Ou»  mark,  0.. 

lOOteL 

licular  1",  aud 

.  always 

Thus 

Deal. 

■ 
■ 

i  <        umfcrmcr. — TIip    eMiUbUOtU 

• 

■  t-idently 

the  fixed  a  i/rr,  o. 
Radius. — 11, 
■ 

all  lino*,  m  o  Imrn  from  tin-  centra  to  the 

il  radii. 

•    li::r,   I.  II,  |m.i*in£  through   tl 

and  liii.  by  the  circui  r.     The 

.  ■  ■(  tin-  radius. 
'  thin   ilir  ebnamfen  i" 

plane  ntrfact,  :■■  any  pari  of  the  circui 

ranti. 

I  -  (he  cirrumfor- 

• 

■  at  the  point  of  contact,  ti. 

I 
i  the  an-  which  count  • 

■  of  the 
■1  wiiliin  an  arc  and  the  chord  which 

I  of  the 

ire  |»  r- 
al  their  inter- 
i   other  withoul 

otfuar  I 

ir  when  formed 
I  fortni  'I  by  two 


pn<trai'tura,  and  rv pnwntvd  in  ti;r«.  | 

tin-    nir  .    anj^c   are    a- 

of  Ilia!!. 

- 

■ 

When  ma  mcaMirv  of  the  a: 

quentl) 

r  when  the  «ir, 

and  taili  inih  . 

l 

■ 
I 

•  .'ii  the 
circle  indicating  the  no  It 

will  l«-  aeen  thai  the  60*. 

those  tl 

other.    Tlir  ri 

t.>  the  m -rtir.-il  line,  ic,  or  the  horizontal  lint 

/'  i 

other  when  tl 

length  ;  the  II  •  Del 

/ 

i  .  when  tlir  i1 

. 
and  '.  : 
when  tli<'  tlir.  i 

it  wiim  an)  i 
funn  n  I 
subtend  Irumcnt 

i 

. 
i|  the  other 

/■  \ 

I  o  when  all  the 

and  il>-  \ 

,\ 
\ 


■ 


BOOK    'IF    INDUSTRIAL   DESIGN. 


aai  da,  Bg.  10.  are  equal  and  perpendicular  to  one  another,  the 
angles  consequently  also  being  equal,  and  all  right  angles. 

A  rectangle  is  a  quadrilateral,  having  two  aides  equal,  as  a  b 
and  r  n,  fig.  14.  and  perpendicular  to  two  other  equal  and  parallel 
sides,  as  a  y  ami  E  N. 

A  parallelogram  is  a  quadrilateral,  of  which  the  opposite  sides 
and  angles  are  equal ;  and  a  lozenge  is  a  quadrilateral  with  all  the 
sides,  but  only  the  opposite  angles  equal 

A  trapezium  is  a  quadrilateral,  of  which  only  two  sides,  as  a  i 
and  M  i..  fig.  9.  are  parallel. 

Polygons  are  regular  when  all  their  sides  and  angles  arc  equal, 
and  are  otherwise  irregular.  All  regular  polygons  are  capable  'if 
being  inscribed  in  a  circle,  hence  the  great  facility  with  which  they 
may  be  accurately  delineated, 

OBSERVATIONS. 

Wo  have  deemed  it  necessary  to  give  these  definitions,  in  order 
to  make  our  descriptions  more  readily  understood,  and  we  propose 
DOW  to  proceed  to  the  solution  of  those  elementary  problems  with 
which,  from  their  frequent  occurrence  in  practice,  it  is  important 
that  the  student  should  be  Well  acquainted.  The  first  step,  how- 
ever, to  be  taken,  is  to  prepare  the  paper  to  be  drawn  upon,  so 
that   it   shall   be  Well    stretched   on    the    board.      To   effect   this,  it 

must  be  slightly  but  equally  moistened  on  one  aide  with  a  sponge; 

the  moistened  Side  is  then  applied  to  the  board,  and  the  edges  of 
the  paper  glued  or  pasted  down,  commencing  with  the  middle   of 

the  sides,  and  then  Becnring  the  corners.  When  the  Bheel  is  dry, 
it  will  bo  uniformly  stretched,  and  the  drawing  may  be  executed, 
being  fust  made  in  faint  pencil  lines,  and  afterwards  redelineatcd 
pi  ii.  To  distinguish  those  lines 
which  may  be  termed  working  lines,  as  being  but  guides  to  the 
in   o(  the  actual  outlines  of  the  drawing,  we  have   in    the 

plates  represented  the  former  bj  i  itted  I  nea,  and  the  latter  by  full 

continuous  lines. 

PROBLEMS. 

1.  To  erect  a  perpendicular  on  the  centre  of  a  given  right  I 
c  D,  Jig.  1. — From  the  extreme  points,  c,'  n,  as  centres,  and  with  a 
radius  greater  than  half  the  line,  describe  the  ares  which  cr 

other  in  a  and  u,  on  either  side  of  the  line  to  be  divided.  A  line. 
a  is,  joining  these  points,  will  be  a  perpendicular  bisecting  the  line, 

C  D,  in  G.     Proceeding  in  the  same  manner  with  each  half  of  the  line, 
I   G  D,  we   obtain    the   perpendiculars,  I  K   and    i.  M,  dividing 

the  line  into  four  equal  parts,  and  we  can  thus  divide  any  given 
right  line  into  2,   1,8,  16,  &c.,  equal  parts.    This  problem  is  of 

ml  application  iii  drawing.    For  instance,  in  order  to  obtain 

the  principal  lines,  V  X  and  V  /..  which  divide  tho  sheet  of  paper 
into  four  equal  parts;  with  the  points,  r  s  I  u,  taken  as  near  the 
edge  of  the  paper  a3  possible,  as  centres,  we  describe  tin  arcs 
which  intersect  each  other  in  p  and  q:  and  with  these  last  as 
centres,  describe  also  the  arcs  which  cut  each  other  in  y,  z.  The 
right  lines,  v  x  and  Y  z,  drawn  through  tho  points,  P,  Q,  and  ;/.  :. 
respectively,  are  perpendicular  to  each  other,  and  serve  as  guides 
in  drawing  on  different  parts  of  the  paper,  and  are  merely  pencilled 
in,  to  be  afterwards  effaced. 

2.  To  erect  a  perpendicular  on  any  given  point,  as  H,  in  the  line  c  D, 


fig.  1 — Mark  oil*  on  the  line,  on  each  side  of  the  point,  two  equal 
distances,  as  c h  and  kg,  and  with  the  centres  c  and  g  describe 
the  arcs  crossing  at  I  or  ic.  and  the  line  drawn  through  them,  and 
lie  'in  h  the  point  it.  will  be  the  line  required. 

3.   To  let  fa  ular  from  a  point,  as  L,  apart  from 

(he  right  line,  c  n. — With  the  point  l,  as  a  centre,  describe  an 
arc  which  cuts  the  line,  c  D,  in  G  and  d,  and  with  these  points  as 
centres,  describe  two  other  ares  cutting  each  other  in  u,  and  the 
right  line  joining  L  and  M  will  be  the  perpendicular  required.  In 
practice,  such  perpendiculars  are  generally  drawn  by  means  of  an 
an    e  and  a  square,  or  T-square,  such  as  fig.  (p1. 

■I.  To  <li  mi-  parallels  to  any  given  li7ies,  as  vx  and  r  z. — For 
regularity's  sake,  it  is  well  to  construct  a  rectangle,  such  as  rst  tj, 
on  the  paper  that  is  being  drawn  upon,  which  is  thus  done: — From 
the  points  v  and  x,  describe  the  arcs  R,  s,  T,  u,  and  applying  tho 
rule  tangentially  to  the  two  first,  draw  the  line  r  s,  and  then  in  tho 
the  line  t  u.  The  lines  r  t  and  s  u  are  also  obtained 
in  a  similar  manner.  In  general,  however,  such  parallels  are  moro 
quickly  drawn  by  means  of  the  T-square,  which  may  be  slid  along 
the  edge  of  the  board.  Short  parallel  lines  may  be  drawn  with 
the  angle  and  rule. 

5.  To  dh  ide  a  given  right  line,  as  a  b,  Jig.  3,  into  several  equal 
parts. — We  have  already  shown  bow  a  line  may  be  divided  into  2 
or  1  equal  parts.  We  shall  now  give  a  simple  method  for  dividing 
a  line  into  any  number  of  equal  parts.     From  the  point  a,  draw 

a  o,  making  any  convenient  angle  with  a  b  ;  mark  off  on  A  C 
as  many  equal  distances  as  it  is  wished  to  divide  the  line  A  u  into; 
in  the  present  instance  seven.  Join  c  B,  and  from  the  several 
points  marked  off  on  a  c,  draw  parallels  to  c  B,  using  the  rule  and 
angle  for  this  purpose.  The  line  a  b  will  be  divided  into  seven 
equal  parts  by  the  intersections  of  the  parallel  lines  just  dmwn. 
Any  Line  making  any  angle  with  a  e,  as  A  i.  may  be  employed  in- 
of  a  e.  with  exactly  the  same  results.  This  is  a  very  useful 
problem,  especially  applicable  to  the  formation  of  scales  for  the 
reduction  of  drawings. 

6.  A  scab  is  a  straight  line  divided  and  subdivided  into  feet, 
inches, and  parte  to  English  measures;  or  into 

li  ii.s.    centimetres,   and  millimetres,   according   to 
French  :i  e  divisions  hearing  the  same  proportion  to 

each  other,  as  in  the  system  of  measurement  from  which  they  are 
derived.  The  object  of  the  scale  is  to  indicate  the  prop  trtiou  the 
drawing  bears  to  the  object  represented. 

7.  To  construct  a  scale. — The  French  scale  being  the  on* 
adopted  in  this  work,  it  will  be  necessary  to  state  that  the  mitr» 
(=39-371    English   inches)  is  the  unit  of  measurement,  and  is 

divided  into  In  deeiuii  lies,  i •,  minu'-tres,  and  1000  millimetre*. 

If  it   is  intended   to  execute  the  drawing  to  a  scale  of  i  or  J;   llie 

metre  is  divided  by  4  or  5,  one  of  the  divisions  being  the  ten 
metre  on  the  reduced  scale.  A  line  of  this  length  is  drawn  on  the 
paper,  and  is  divided  into  reduced  decimetres.  &c.  just  as  the. 
in.tre  is  itself.  Fig.  7  is  part  of  a  scale  for  reducing  a  drawing  to 
In  this  scale  an  extra  divisi  in  is  placed  to  the  left  of 
zer...  wbi.-li  is  subdivided,  to  facilitate  the  obtainment  of  any  re- 
quired measure.  F..r  example,  if  we  want  a  length  corresponding 
to  33  centimetres,  we  place  one  point  of  the  compasses  on  the 
division  marked  3  to  the  right  of  zero,  and  the  other  on  the  second 


I 


Tiir.  pn\<Ti«\i.  DRAroirrsMAVS 


drrbtoa  to  the  left,  and  the  length  comprised  between  these  points 
will  be  3  dVrimAtrrv  3  een  ime-tre*.  =  S3  centimetres. 

The  ahiigissci  ttmte  :nnule  im-»«un ments  are  n- 

qiuosi  greater  precision  is  obtained  with  a  diagonal  scale,  such  aa 
fig.  ft.     It  b  thu»  constructed : — Having  drawn  a  line  ami  i 
it.  at  in  fig  7,  draw,  parallel  and  equal   to  it,  tin 
c  <£  a./,  if.,  at  c^aal  distances  apart, 
dkrulan  at   tl  I 

dKWooa   to    tl  .  draw  the  flBMjnnal.   .'■  i.  and   draw 

pualleb  to  it  from  the  mnainii 
From  the  di». 

to  the  point  on  the  extreme  parallel.  ■  4.  rut  by  '' 
dicular,  and  draw  also  the  parallel  diagonals,  1 — 2.  2 — 3.  aa  I 

It  will  be  evident,  that  aa  in  the  space  of  the  ten  borizoata]  line  % 

the  left,  it  w: 
intermediate  11:  .1.  3d,  die.,  at  •   1.2.3. 

h»  of  such  di\i«i.>n.  in    the   same  direction,  so   that    the 
diagonal  line,  3'.  will  cut  the  5th  line  at  a  point  2,*,  of  ■  d 
diatant  from  zero.     Tl 
on  the  point  i,  and  tin-  other  on  Iha  Intersection  of  111 

la]  line  with  the  perpendicular  of  il 
the  measure  compriaed  between  t ii -  m  will  be  3  <1< 

■ad  ,'..  .T  5  millimetre*  =  325  mili.: 
/  I  angle,  as  T  c  n,  fig.  2,  inln  tw»  eipiu 

!ie  apex,  c,  as  a  centra,  deeeribe  tha  arc,  h  i.  and  willi  Iha 

-  cutting 
each  other  in  ; ;  join  ;  c,  and  the  right  line,  j  < .  will  bifida  tha 

-    ii  i  j  and  i  i  i.    Tl. 
be  sublividcd  in  the  aame  manner,  aa  shown  in  '! 
angle  may  alao  be  divided  by  BMaoa  of  either  of  i: 

D.  *■ 

9.   To  drate  a  tangent  m  n  _  n  D  H,  fig.  X 

required  to  draw  iha  in  the 

.  radius,  c  D,  must  be  drawn  meeting  llie  point,  and   be   pro- 
duced beyond  it,  «ay  to  e.    Then,  by  Iha  method  dread] 
draw  2  |<vndicular  to   c  E,  cutting  it   in   t>,  anil  it 

will  be  ,  linst      If.  h    •• 

the   ta:  I    given    point,  a*    a,  oataidl     Iha    circle,  a 

awn  joining  the  point,  a,  an  : 
of  the  I  '  the  point,  0,  with  this 

point   »•  -  nl»'  a  circle  passing  through  A  nn-; 

"  in  n  and  it :  right   lines  joining  a  ii  and 
A  M  wi  '  •,  circle,  and  lb 

•  ad  and  a  ii  respectively. 
'  -ill  u-ith  irhirh 

•    drawn. — With    an;. 
aa  centres,  describe  arcs  of  equal  limiaa,  entdng  each  othi 
throogh  the   ;.  ..  to  and   L0J 

o,   the 


11/  "-It  through  any  three  points  ru*  in  a  right 

irelo  can  |«ss  through  the  aa:; 
and  sir.  g    (he  centre  :- 

and  a  point  in  the  cir 
exactly  the  ami  • 

/'.  iiucn&r  a  cirxle  m  a  guen  triangle,  as  a  ■  r,  fig.  6. — 


srribej  in  a  figure,  when  all  ,; 

latter  an 

lines,  as  a  a  B  ' 

fall   per;-  — e  per- 

..il,  and  radii  of  the   r. 

Ii     V    .      i  jV  .i  :'i.j'i_->.  .i<  0  u.  '  -  ,ual  }<arts. — If 

the  parts  an-  n  le,  as  g  t,  in  the 
with  which,  aa 

i 

k,  b]  the  perpenrhcahg  I .  equal 

and  draw  ma  One,  i.  m.  |wralM  to  ii  i.  Tha  trtangli 
■ 
■  half  the  Mangle,  g  ii  t.     If  the  given  triangle  were  cm, 

it  eroold  alao  be  dhrhlad  into  two  equal  parti  i  m. 

I  I     Ih  ilrair  a  tmttn  diruhle  (Ac  >  I  [uarr,  A  B  r  D, 

rtrnara   any  two  sidea 

srUefa  are  at  ri.-tit  angina  to  each  other,  a"  n  A  and  D  C,  to  n  and  L, 

with  Iha  ci  utre,  n,  and  radius,  i.  n.  .1.  rjnailaf 

and  through  llie  pot 
-.  i>  a  and  D  i..  draw  parallels  to  d  l  and  da  reapectirejy,  or 
i  g  e  p,  will  be  double 
i  of  Iha  given  square,  a  bc  d;  and  in  the  aama  manner  a 

ii  K  I.  n,  may   be   drawn  double   the  area  of  On     • 
Il  i*  evident  that  the  diagonal  of  ■  •  iual  to 

one  -i  le  of  a  square  twice  (hi 

15.    Tn  ittCtibt  a  rirrlr  half  the  tea)  nf  a  giien  rirrle.  ihkid, 
•Draw   two  diameters,  a  n  and  r  t»,  at  right  ai 
each  other;  join  an  extremit]  the  chord)  ac 

tl  is  chord  by  tin-  perpendkolar,  r.  r.    The  radius  of  tin 

'.  circle  will  l«    ■  It  follow,  that   the  annulai 

rnal  to  Iha  amaOer  oirde  wHUn  it. 

11.        '/'•      I',-.-!'  13, 

ii  — Draw  any  diameter, 0  r,  and  with 
g,  as  a  centre,  oV  aariba  Iha  an-,  inn.  its  radius  being  equal  to  thai 

of  the  gi\m  circle;   join    D  r.  I  r,  and    I   D,  and    D  »"•  T  will   be  the 
r.qiiinsl.     The  ~i.le  of  a  M  gular  hi  to  the 

r  the  eirenmacribing  drele,  and,  therefore,  in  order  to  in- 

sci-ilic  it  in  a  drele,  all  that  is  necessary  is  to  mark  olT  00  lln-  cir- 
cunili  nncc  the  length  of  the  radius,  and,  joining  the  |K.ints  of  in- 

n,  as  k  1 1.  ii  m  j,  the  naulaTuH,  figure  will  Is-  iha  i 
T  ■     -  -i'  •   H  •  ■■■  i  of  19  or  '2i  -il. «.  ii  i-  mi 
to  dhrlde  or  lubdiride  the  ■ 

i   ;is  alM.ve.  and  to  join  the  |>oitits  of  intl 
■ 
mil.  and  bottb  I 

I  '■<•  ,  Hi  whi.l  ..  or  the  stjuara. 

in  differ  -  bdtaatod  m  " 

17.  T  '  '■  ''-    13  — 

-  a  ii.  0  D,  perpaooaaahv  to  one  another,  aru 
join  the  |>oini-  •  ■<■.  and  A  i;  ii  i>  will  be 

ind. 
1»     7'.     •  I    i.V  a  regular  octagon  abrntt  a 

II    .nig.  as  in    the   last   OBCC,  ilr.iun    '«•> 
i    i,    ,.  ii.    draw    other   tw...    i  j.    k  : 
■    mud  l,y  the  t'..niur;  through  the  i  igh!  p..inls  ol  u.ierws;- 


BOOK   OF    INDUSTRIAL   DESIGN. 


tion  with  the  circle  draw  the  tangents,  e,  k,  e,  j,  f,  i..  i — these  tan- 
gents "ill  cut  each  other  and  form  the  regular  octagon  required. 
This  figure  may  also  be  drawn  by  means  of  the  square,  and  angle 
of  45",  ©. 

19.  To  construct  a  regular  octagon  of  which  one  side  is  given,  as 
A  V,fig.  14. — Draw  the  perpendicular,  o  u,  bisecting  a  b  ;  draw  A  F 
parallel  to  o  d,  produce  a  n  to  C,  and  bisect  the  angle,  c  a  f,  by  the 
line  e  a,  making  E  a  equal  to  a  b.  Draw  the  line  og,  perpendi- 
cular to,  and  bisecting  e  a.  oq  will  cut  the  vertical,  o  d,  in  o, 
which  will  be  the  centre  of  the  circle  circumscribing  the  required 
octagon.  This  may,  therefore,  at  once  bo  drawn  by  simply  mark- 
ing oft'  arcs,  as  E  H,  H  f,  &c,  equal  to  A  B,  and  joining  the  points, 
F..  h,  f,  &c.  Be  dividing  and  subdividing  the  arcs  tints  obtained 
we  can  draw  regular  figures  of  16  or  32  sides.  The  octagon  is 
a  figure  of  frequent  application,  as  for  drawing  bosses,  bearing 
brasses,  &c. 

20.  To  construct  a  regular  pentagon  in  a  g  inn  <  ircle,  as  A  B  c  D  F, 
also  a  decagon  in  a  gken  circte,  as  E  R  to,  fig.  15. — The  pentagon 
is  thus  obtained  :  draw  the  diameters,  A  t,  B  J.  perpendicular  to  each 
other;  bisecting  OE  in  K.  with  K  as  a  centre,  and  k  a  as  radius. 
describe  the  arc,  a  l  ;  the  chord,  a  l,  will  be  equal  to  a  side  of  the 
pentagon,  which  may  accordingly  be  drawn  by  making  the  chords 
which  form  its  sides,  as  a  e,  f  d,  d  c,  c  b,  and  b  a,  equal  to  a  l. 
By  bisecting  these  arcs,  the  sides  of  a  decagon  may  be  at  once 
obtained.  A  decagon  may  also  be  constructed  thus : — Draw  two 
radii  perpendicular  to  each  other,  as  o  M  and  o  R ;  next,  the  tan- 
gents, N  M  and  N  R.  Describe  a  circle  having  N  H  for  its  diameter  ; 
join  K,  and  f  the  centre  of  this  circle,  the  line,  R  p,  cutting  the 
eircle  in  a ;  r  a  is  the  length  of  a  sido  of  the  decagon,  and  applying 
it  to  the  circle,  as  r6,  &c.,  the  required  figure  will  be  obtained. 
The  distance,  r  a  or  rc,  is  a  mean  proportional  between  an  entire 
radius,  as  r  n,  and  the  difference,  c  N,  between  it  and  the  radius. 
A  mean  proportional  between  two  lines  is  one  having  such  relation 
to  them  that  the  square,  of  which  it  is  the  one  side,  is  equal  to  tire 
rectangle,  of  which  the  Other  two  are  the  dimensions, 

21.  To  construct  a  rectangle  of  which  the  sides  shall  be  mean  pro- 
portionals between  a  given  line,  as  A  c,  fig.  16,  and  oiw  a  third  or 
two-thirds  of  it. — A  c,  the  given  line,  will  be  the  diagonal  of  the 
required  rectangle;  with  it  a-s  a  diameter  describe  the  circle  abcd. 
Divide  A  c  into  three  equal  parts  in  the  points,  m,  n,  and  from  these 
points  draw  the  perpendiculars,  m  D  and  n  B  ;  the  lines  which  join 
the  points  of  intersection  of  these  lines  with  the  circle,  as  A  B,  a  d, 
c  b,  c  d,  will  form  the  required  rectangle,  the  side  of  which,  c  D,  is 
a  mean  proportional  between  c  m  and  c  A,  or — 

Cm:  CD::CD:CA; 
that  is  to  say,  the  square  of  which  C  D  is  a  side,  is  equal  to  a  rec- 
tangle of  which  c  a  is  the  length,  and  c  m  the  height,  because 

CDxCD  =  CmxCA* 
In  like  manner,  a  d  is  a  mean  proportional  between  c  a  and  m  a. 
This  problem  often  occurs  in  practice,  in  measuring  timber.  Thus 
the  rectangle  inscribed  in  the  circle,  fig.  16,  which  may  be  con- 
sidered as  representing  the  section  of  a  tree,  is  the  form  of  the 
beam  of  the  greatest  strength  which  can  bo  obtained  from  the 
tree. 

*  See  the  notes  and  rules  given  at  the  end  of  thu  chapter 


APPLICATIONS. 

DESIGNS   FOR    INLAID   PAVEMENTS,  CEILINGS,  AND    BALCONIES. 

PLATE    II. 

The  problems  just  considered  are  capable  of  a  great  variety  of 
applications,  and  in  Plate  II.  will  be  found  a  collection  of  some  of 
those  more  frequently  met  with  in  mechanical  and  architectural 
constructions  and  erections.  In  order,  however,  that  the  student 
may  perfectly  understand  the  different  operations,  we  Would 
recommend  him  to  draw  the  various  designs  on  a  much  larger 
scalo  than  that  we  have  adopted,  and  to  which  we  aro  necessarily 
limited  by  space.  Tho  figures  distinguished  by  numbers,  and 
showing  the  method  of  forming  the  outlines,  arc  drawn  to  a  larger 
scale  than  the  figures  distinguished  by  letters,  and  representing  tho 
complete  designs. 

22.  To  draw  a  pavement  consisting  of  equal  squares,  figs.  A  and 
1. — Taking  the  length,  a  b,  equal  to  half  the  diagonal  of  tho 
required  squares,  mark  it  off  a  number  of  times  on  a  horizontal 
line,  as  from  A  to  B,  B  to  c,  &e.  At  A  erect  the  perpendicular 
I  h,  and  draw  parallels  to  it,  as  D  E,  G  f,  &c,  through  the  several 
points  of  division.  On  the  perpendicular,  i  H,  mark  off  a  number 
of  distances  equal  to  A  B,  and  draw  parallels  to  A  B,  through  tho 
points  of  division,  as  h  g,  I  f,  &c.  A  series  of  small  squares  will 
thus  be  formed,  and  the  larger  ones  are  obtained  simply  by  draw- 
ing the  diagonals  to  these,  as  shown. 

23.  To  draw  a  pavement  composed  of  squares  and  interlaced 
rectangles,  figs.  (5)  and  2. — Let  the  side,  as  c  d,  of  the  square  bo 
given,  and  describe  the  circle,  L  M  q  B,  the  radius  of  which  is  equal 
to  half  the  given  side.  With  the  same  centre,  o,  describe  also 
the  larger  circle,  K  N  P  i,  the  radius  of  which  is  equal  to  half  the 
side  of  the  square,  plus  the  breadth  of  the  rectangle,  a  b.  Draw 
the  diameters,  a  c,  e  d,  perpendicular  to  each  other ;  draw  tan- 
gents through  the  points,  a,  d,  c,  e,  forming  the  square,  jhfo; 
draw  the  diagonals  J  F,  g,  h,  cutting  the  two  circles  'n  the  points, 
I,  B,  K,  L,  M,  N,  P,  Q,  through  which  draw  parallels  to  the  diagonals. 
It  will  be  perceived  that  the  lines,  a  e,  e  c,  c  d,  and  D  a,  aro 
exactly  in  the  centre  of  the  rectangles,  and  consequently  serve  to 
verily  their  correctness.  The  operation  just  described  is  repeated, 
as  far  as  it  is  wished  to  extend  the  pattern  or  design,  many  of  the 
lines  being  obtained  by  simply  prolonging  those  already  drawn. 
In  inking  this  in,  the  student  must  be  very  careful  not  to  cross  tho 
lines.  This  design,  though  analogous  to  the  first,  is  somewhat 
different  in  appearance,  and  is  applicable  to  tile  construction  of 
trellis-work,  and  other  devices. 

24.  To  draw  a  Grecian  border  or  frieze,  figs.  ©  and  3. — On  two 
straight  lines,  as  a  b,  ac,  perpendicular  to  each  other,  mark  off, 
as  often  as  necessary,  a  distance,  a  t,  representing  the  width,  ef, 
of  the  ribbon  forming  the  pattern.  Through  all  the  points  of 
division,  draw  parallels  to  a  b,  a  c — thus  forming  a  series  of  small 
squares,  guided  by  which  the  pattern  may  be  at  once  inked  in, 
equal  distances  being  maintained  between  the  sets  of  lines,  as  in 
fig.  ©.  This  ornament  is  frequently  met  with  in  architecture, 
being  used  for  ceilings,  cornices,  railings,  and  balconies;  also  in 
cabinet  work  and  machinery  for  borders,  and  for  wood  and  irori 
gratings. 

25.  To  draw  a  pavement  composed  of  squares  and  regular  octa. 


' 


gvm.fig*.  D  atj  i.—  W 

in»!e  I.,  draw 
i: — iuc   »quare,  a  a  c  D,  being  timt    obtained,  mii-i 
ICID,  drawn 
bring  then  -ir.. 
be  formed  by  marking  off  from  each  • 

pattern  u  extended  rimpty  by 

ride*  of  four 
which   an-  inclined  at  an  an 
ThU    pt  ■  •»!'•  marble, 

Bl     CuluUTH,    «). 

36.   7'  icti/  composnl 

and  5.- 

6 
'. 

■ 
the  hexagon*  are   plain  and   shad.  :  m    their 

arranj> ::  •    !"iir. 

. 
Bqvarti, 

nala,  A  c,  B  d  ;  i 

the  firv.    '  rial,  r  d,  mark  the  equal  rthrtanceo,  or,  if,  and 

through  c  and /draw  parallel*  tn  tlir  diagonal,  a  c  ;  join  th* 

'  ilea,  i  /. 
m  n,  erl  1  to  form  Ihi    | 

requirir  - 

!h    Formed  in 

I  f..r  furnitiu. 

On  a  ■trai'rrht  line,  A  B.  mark  off  Ihi 

aw  Ike  due 1  d, 

•■ad:  and  draw   a  i 
I  r  parallel  to  A  B.     C  .  i .  cut- 

i  jobi a  ii.     In  Ihii 

■  I  by  continuing 
the   line*   and  drawing   parallel!  n- 

remain  .  -  rn    will   In-   r> 

I 

ami  12. — If  in  ' 

diagnnv  shall  obtain 

■ 

I  be  tlir 
*]*•%  of 

•  lint*. 

vrangeinent*  of  >ari»u<  regular  pol 

pattern*  may  be  produced  by  combining  these  d 


■!  many  art*,  particularly  for 

.mental 

/      aVair  an  open-work  •ting  of  Uaenget  and 

'i.'».  H  andS-   . 

I 

lii.li  mast  ihi  li.'ular 

./,  draw   parallela  to 
■ 

•  .i|ur1.      The  i'  lie  the 

•  r  mat 

ti  radii. 

I  •.,••....  I  by  ad  •  -.  and  to 

•  a,  parallel*  to 
drawn,  then  ■  cora- 

ttern. 

.  composed  if  imall  squares  or 
md  9.— 
1 
nt'  roar  of  the  amall  loxcngea,  draw  tl  • 

Into  t'"Ur  equal    part* 
iil"  the  I  ^  ii.  ami  join 

.  /«,  are 
..ml  tin-  appropriate  iiarallel-  I 
drawn.     In  extending  the  pattern  bj  repetition,  Ihi 
ponding  t.>  i  ai 
parallel  line*,  as  i  i  and 

I 
i  aeh,  a  Dumber  of  pattern*  may  l«-  | 

though  formed  of  tie 

rn,  eom- 
:  rililxins  intrrla 

1 

l«-  drawn.  uilh 

vertical  i  ■  -.  make  i  i  equal  t"  i  a.  and  «.■ 

the  circle  havL 

equal  ■  ■!.-■  I ' 

which  will  complete  the  lit 
of  tlir  pattern,  |,  u,  the  left.    Ti. 

duplex,  fig    9,  may  1-  "n  tlio 

V.  -  are  run 

int..  pal  I    tin-in 

join  «•■!!.  aa  the  beauty  of  Ihe  dra 

mk  in  the  •  H  i*  practieaDy 

Kan  tn  draw  a 

•  line. 

/  mjnifrii 

1  I    1  WO 

i.tli  aba 

■  -  ..i  the  other,  dm  Brat  the 

•   I  tin'  inner  and  coneentric  one,  *fgn.    Tlio 

I   tin'  latter  being  eul  bj  tie  and  ID,  la  the 

i.  ;.  k.  I,  IhrOUgh  (heme  draw    |>nrallcl»  to  the  ride*  of  tho 

aquare,   abcd,  and  finally,  with   the  centre,  o,  describe  a  amaV 


ROOK  OF  INDUSTRIAL  DESIGN. 


circle,  the  diameter  of  which  is  equal  to  the  width  of  the  ind 
crosses,  the  sides  of  these  being  drawn  tangent   to  this  circle. 
Tims  are  obtained  all  the  Hues  accessary  to  delineate  this  pattern  : 
the  relievo  aud  intaglio  portions  are  contrasted  by  the  latter  being 
shaded. 

In  the  foregoing  problems,  we  have  shown  a  few  of  the  manj 
varieties  of  patterns  producible  by  the  combination   of 

regular  figures,  lines,  and  circles.  There  is  DO  limit  to  the  multi- 
plication iif  these  designs;  the  processes  of  construction,  however, 
being  analogous  to  those  just  treated  of,  the  student  will  be  able 
to  produce  them  with  every  facility. 

SWEEPS,  SECTIONS,  AND  MOULDINGS. 
PLATE  III. 

34.  To  draw  in  a  square  a  a  rtss  of  arcs,  relisted  by  semicircular 
mouldings,  figs.  A  and  1. — Let  a  B  be  a  side  of  the  square  ;  draw 
the  diagonals  cutting  each  other  in  the  point,  o,  through  which 
draw  parallels.  D  E,  c  F,  to  the  sides;  with  the  corners  of  the 
square  as  centres,  and  with  a  given  radius,  a  <;,  describe  the  four 
quadrants,  and  with  the  points,  D,  F,  B,  describe  the  small  semicircks 
of  the  given  radius.  D  <;,  which  must  be  less  than  the  distance,  D  b. 
This  completes  the  figure,  the  symmetry  of  which  may  be  verified 
by  drawing  circles  of  the  radii,  c  G,  c  H,  which  should  touch,  the 
former  the  larger  quadrants,  and  the  latter  the  smaller  semi- 
circles. If.  instead  of  the  smaller  semicircles,  larger  ones  had 
been  drawn  with  the  radius.  D  i,  the  outline  would  have  formed  a 
perfect  sweep,  being  free  from  angles.  This  figure  is  often  met 
with  in  machinery,  for  instance,  as  representing  the  section  of  a 
beam,  connecting-rod,  or  frame  standard. 

35.  To  draw  an  arc  tangent  to  two  straight  lines. — First,  lei  the 
radius,  a  b.  fig.  3,  be  given;  with  the  centre,  A,  being  the  point 
of  intersection  of  the  two  lines,  A  B,  A  c,  and  a  radius  equal 
to  a  b,  describe  arcs  cutting  theso  lines,  and  through  the  points  of 
intersection  draw  parallels  to  them,  B  o,  c  o,  cutting  each  other  in 
o,  which  will  be  the  centre  of  the  required  arc.  Draw  perpen- 
diculars from  it  to  the  straight  lines,  A  B,  AC,  meeting  them  in 
D  and  E,  which  will  be  the  points  of  contact  of  the  required  arc. 
Secondly,  if  a  point  of  contact  be  given,  as  B,  tig.  3,  tie  lb*  a 
being  A  B,  AC  mating  any  angle  with  each  other,  bisect  the 
angle  by  the  straight  line,  a  d  ;  draw  B  o  perpendicular  to  a  n,  from 

the  point,  b,  and  the  point,  o,  of  its  intersection  with  a  d,  will  be 
the  centre  of  the  required  arc.  If.  as  in  figs.  -  and  :i.  we  draw 
arcs,  of  radii  somewhat  less  than  o  B,  we  shall  form  conges,  which 
stand  out  from,  instead  of  being  tangents  to.  the  ui\  >n  straight 
lines.  This  problem  meets  with  an  application  in  drawing  fig.  2- 
which  represents  a  section  of  various  descriptions  of  castings. 

36.  To  draw  a  circle  tangent  to  three  given  straight  lines,  which 
make  any  angles  with  cocA  other.  Jig.  4. — Bisect  the  angle  of  the 
lines,  ab  and  A  c,  by  the  straight  line,  A  E.  and  the  angle  formed 
by  c  d  and  c  a,  by  the  line,  c  f.     a  e  and  c  f  will  cut  each  other 

in  the  point,  o,  which  is  at  an  equal  distance  & -a.h  side,  and 

is  consequently  the  centre  of  the  required  circle,  which  may  be 
drawn  with  a  radius,  equal  to  a  line  from  the  point,  o,  perpendi- 
cular to  any  of  the  sides.  This  problem  is  necessary  for  the  com- 
pletion of  n>.  @. 


37.  To  draw  the  section  of  a  stair  rail,  Jig.  ©. — This  gives  riso 
to  the  problems  considered  in  tigs.  5  and  6.  First,  let  it  be  ro- 
quired  to  draw- an  arc  tangent  tii  a  given  arc,  as  a  b,  and  to  the 

given  straight  line,  CD,  tig.  •> — D  being  the  point,  of  contact  wi  h 
the  latter.  Through  u  draw  E  F  perpendicular  to  CD;  make  FD 
equal  to  OB,  the  radius  of  the  given  arc,  and  join  or,  thlOUgh 
the  centre  of  which  draw  the  perpendicular,  G  E,  and  the  point,  E,  of 
its  intersection  with  i:  r,  will  be  the  centre  of  the  required  arc, 
aud  ED  the  radius.  Further,  join  o  E,  and  the  point  of  intersec- 
tion, i),  with  the  arc,  A  n,  will  be  the  point  of  junction  of  the  two 
arcs.  Secondly,  let  it  be  required  to  draw  an  arc  tangential  to  a 
given  arc,  as  All,  and  to  two  straight  lines,  as  bc,cd,  fig.  5. 
Bisect  the  angle,  ii  c  D,  by  the  straight  line,  C  E  ;   with  the  centre,  C, 

ami  the  radius,  en.  equal  to  that  of  the  given  arc, b a, describe 
the  an',  o  a  ;  parallel  to  ti  <•  draw  t  it  J,  cutting  E  c  in  J.  Join  o  J, 
the  line,  o  j,  cutting  the  arc,  H  g,  in  g  ;  join  c  G,  and  draw  o  K  pa- 
rallel to  cg;  tho  point,  k.  of  its  intersection  with  E  J,  will  be 
the  centre  of  tin'  required  arc,  and  a  line.  K  L  or  K  H,  perpendicular 
to  c  ither  of  the  given  Btraight  lines,  will  be  the  radius. 

38.  To  draw  the  section,  (J  an  acorn,  Jig.  ©. — This  figure  calls 
for  the  solution  of  the  two  problems  considered  in  tigs.  ;>  and  10. 

First,  it  is  required  to  draw  an  arc.  passing  through  a  given  point, 
A,  fig.  9,  in  a  line,  a  b,  in  which  also  is  to  be  the  centre  of  the 
are,  this  arc  at  the  same  time  being  a  tangent  to  the  given  arc.  0, 
.Make  a  I)  equal  to  o  c,  the  radius  of  the  given  arc  ;  join  o  D,  and 
draw  the  perpendicular,  f  b,  bisecting  it  B,  the  point  of  inter- 
section of  the  latter  line,  with  A  B,  is  the  centre  of  the  required  ale, 
a  e  c,  a  b  being  the  radius.  Secondly,  it  is  required  to  draw  an  arc 
passing  through  a  given  point,  A,  fig.  10,  tangential  to  a  given  are, 
bcd,  and  having  a  radius  equal  to  a.  With  the  centre,  o,  of  the 
given  arc,  and  with  a  radius,  o  E,  equal  to  o  c,  plus  the  given  radius, 
a.  draw  the  arc  B ;  and  with  the  given  point,  a.  as  a  centre,  and 
with  a  radius  equal  to  <;.  describe  an  arc  cutting  the  former  in  E 
— E  will  be  the  centre  of  the  required  are.  and  its  point  of  contact 
with  the  given  arc  will  be  in  c,  on  the  line,  o  E.  It  will  be  seen 
that  ill  fig.  r£).  these  problems  arise  in  drawing  either  side  of  the 
object.  The  two  sides  are  precisely  the  same,  but  reversed,  and 
the  outline  of  each  is  equidistant  from  the  centre  line,  which  should 

always  be  pencilled  in  when  drawing  similar  figures,  it  being  diffi- 
cult to  make  them  symmetrical  without  such  a  guide.  This  is  an 
ornament  frequently  met  with  in  machinery,  aud  iu  articles  of 
vai  ious  materials  and  uses, 

39.  To  tlruic  a  wan  run,  .formed  by  arcs,  equal  and  tangent  to 
each  other,  and  passing  n  jioinls,  a,  b,  their  radius  being 

distance,  a  b.  figs.  2  and  7. — Join  A  B,  and  draw 
the  perpendicular,  E  F,  bisecting  it  in  C.  With  the  centres,  A  and 
i'.  and  radius,  a  C,  describe  arcs  cutting  each  other  in  Co  and  with 
the  centres,  11  and  c,  oilier  two  cutting  each  other  in  li ;  g  and  H 
will  be  the  centres  of  the  required  arcs,  forming  the  curve  or 
sweep,  Air..  This  curve  is  very  common  iu  architecture,  and  is 
styled  the  eyinu  redo. 

40.  To  draw  a  similar  curve  to  the  preceding,  but  formed  by 
tires  of  n  gixen  radius,  as  a  t.figs.  G?  and  11. — Divide  the  straight 
line  into  four  equal  parts  by  the  perpendiculars,  E  F,  Q  B,  and 
c  D  ;  then,  with  the  centre,  a,  and  given  radius,  A  I,  which  must 
always   be   greater  than   tho   quarter   of  A  B,   describe    the   arv 


0»  ia  c:  alar,  w-iih  ate  centre,  a.  »  aanilir  are  or.mg 
•  a  ia  a ;  c  aad  ■  will  be  lb*  centre*  uf  ibe  am  forawag  the  re- 
quired evil  Whalrter  be  the  given  radios,  protidrd  it  at  not 
too  small,  lha  centres  of  tha  arc*  w  ill  *!»*>»  be  ia  the  fine*,  c  D 
aad  •  a.  It  will  be  aeca  that  the  area,  c  t  and  a  i,  cut  the  straight 
anas,  c»  aad  e  a.  io  two  points  raapiru  lafca  the 

aw  mill  poiata,  uu  centres.  w«  ahall  form  a  ainalar  cane  to  the 
laat,  bat  with  the  concavity  and  convexity  tranepused.  aad  called 
tha  n/ma  rrwra*.  The  two  mill  be  found  ia  fig .  f,  the  firat  at  a, 
aad  the  second  at  a.  This  figure  represents  the  aertioo  of  a 
door,  or  window  bane — it  is  one  well  known  to  carpenter*  aad 

The  little  iaairamrot  ksowa  as  the  -  Cvmameter."  afford*  a 
coot  cnirnt  mean*  of  obtaining  rough  niraaareiDeiita  of  contours 
of  rariooa  classes,  as  mouldings  aad  bas-refiefa.  It  is  amply  a 
Ight  adnsatsble  frame,  acting  as  a  apnea  of  holding  socket  fur  a 
dim  of  paraDet  slips  of  wood  or  metal— a  handle  of  straight 
,  for  example.  Previous  to  applying  tins  for  taking  an  ho- 
of measurement,  the  whole  aggregation  of  pieces  is 
diwsid  in  M  •  at  surface,  so  that  their  eods  form  s 
plane,  like  the  cads  of  the  bristles  in  a  square  rut  brush ;  and 
these  component  piecea  are  held  in  close  parallel  contact,  with  just 
anoafh  of  stiff  friction  to  keep  them  from  slipping  and  falling 
a»  it.  The  ends  of  the  piecea  are  then  applied  well  op  to  the 
»«— t*»g  or  surface  whose  cavities  and  projections  are  to  be  mea- 
sured, and  the  frame  is  then  acrewed  up  to  retain  the  slips  in  the 
araetfon  thus  aaiian  il  The  surface  thus  moulds  ha  sectional 
rontour  upon  the  needle  coda,  as  if  the  surface  made  up  of  theae 
arsis  waa  of  a  plaatie  material,  and  a  perfect  impression  is  there- 
for* earned  a-»av  on  the  instrument.  Toe  nicety  of  delineation  is 
.■■J  by  the  rels 
41  TodiwbaluMtrafm&iflexamltmr,fig*.Qmti' 
here  neeeaaary  to  draw  an  -• 

know*  arcs,  a  i  and  c  r>.  and  <i  bori- 

lootal,  t  i  Eitend  t  i  to  B.  making  i  B  equal  to  c  n.  the  radius 
of  the  are.  c  o.     Join  c  a.  biaectin.-  ■;.»  ndicular;  this 

will  cat  r  B  in  the  point,  e,  which  is  tbr  crntrr  of  the  required  arc — 
« i  being  it*  radius.  A  line  joining  e  a  ruts  c  D  in  c  the  point  of 
contact  of  the  two  area.  The  arc.  t>  r,  which  is  required  to  be  a 
tangent  to  c  n,  and  to  pass  through  the  point,  r,  is  drawn  with  the 
centre,  o,  obtained  by  biaecting  th<  era  ndkabv 

which  cuts  the  radius  of  the  -  ken,  in  fig.  Q.  to 

b*  repeated  both  on  each  aide  of  the  t  crural  line,  m  n.  and  of  the 
t.  ■     aid  ;.:,•  ,fg. 

i;,  irate  tar  aerriow  of*  halajfer  c/siavair  owtirar,  as  fig.  X- 
■  *  an  air  passing  through  two  points,  a,  a, 
'  '  r*  bring  in  a  straight  line,  •  c ;  this  are,  moreover, 

n^uinnjr  to  join  at  n.  and  form  a  sweep  with  another.  :■  i.  hating 
rut  centre  in  a  line,  r  i >.  pars.'  i  ■    ; «  ndicu- 

IV  hiaertiag  ■  A.  will  rut  a  c  in  o,  which  will  br  the  centre  of  the 
firat  arc.  and  that  of  the  second  may  now  be  obtained,  aa  in 
prohlaat  37.  fig.  6 

.'-•*  base  of  the  baluster,  fig.  H.  ia  in  the  form  of  I 
tanned  a   aces*.     It  may  be  drawn    by  taitowa  untbuda.     The 
fallowing   are  two   of  the   airnptrwl     areording  to  the  firat.  the 
aajre*  may  be  formed  by  area  awerping  into  each  other,  and  tan- 


geataat  a  aad  c  U  tare  given  aaraMs,  a,  a,  en,  fig.  IX  Through 
fiaaj  the  prrpcadkaars,  c  o  aad  a  k,  aad  divide  the  latter 
into  three  equal  parts.  With  one  drriaoa,  F  a,  aa  a  radian, 
•  U  first  arc,  a  c  b  ;  totX.tr  c  t  eqaal  to  r  A.  join  l  r,  aad 
bisect  I  r  bj the  nvrpradkahu-.  o  x.  which  cuts  c  0  ia  a  o  will 
br  the  eratre  of  the  other  arc  required.  The  Bar,  o  a,  paeanf 
through  the  centres,  o  and  r,  wil]  cat  the  area  in  the  point  of  junc- 
tion, a.  It  is  at  this  manner  that  the  cunre  ia  fig.  N  a  ibtaaii 
The  aeroad  method  a  to  form  the  carve  by  two  area  sweeping 
into  each  other  and  pawning  through  the  given  poiata.  a  a,  fig.  14, 
their  centres.  b»w  r » er.  being  in  the  anae  b.  <m  ■  •atal  fine,  c  n, 
parallel  to  two  ai  eight  lines,  x  r  aad  a  c,  pawning  tatoagh  tha 
given  poiata.  Throagfa  a,  draw  the  pcrprocacwlnr,  A  L  I.  a*  point 
of  interarcaoo  with  c  It,  ia  the  eratre  of  oar  are,  a  t>.  Ml  it  draw 
the  chord,  a  n,  the  perpendicular  brarrting  whs-h.  will  cut  c  n  ia  o, 
the  centre  of  the  other  arc,  the  rail  us  being  o  D  or  o  a.  Thia  curve 
is  more  particalarly  met  with  in  the  conatraraoa  of  bases  of  tat 
i    riiriusn.  and  Cocnposite  order*  of  arduteeture. 

•••  Tcustom  the  stodrnt  to  propca-aoa  hi*  deaigaa 
to  the  rules  adopted  ia  practice  ia  the  awre  ulnioa*  appriratvtna, 
we  bate  indiratrd  on  each  of  the  figs.  A-  3-  C  &<-.  aad  oa  tha 
•ding  outlines,  the  measurrmen t»  of  the  varioa*  pans,  ia 
aaftaaetrea.  It  mast,  however,  at  the  same  time  ha  understood, 
that  the  various  piobWra  are  equally  capable  of  aulaaua  with 
other  data:  and.  indeed,  the  number  of  applications  of  which  tha 
:  •  -  •  -■-.  ..•  *--•,-•  .._-■--•-  -  .  -.. 
■ 


:  KNTARY  '  R06       TK& 

PLATE   IV. 
4*    Having  solved   the   foregoing  pi  iiblian,  tha   itaial  may 

i!  : 

- 
to  the  accurate  determination  of  tha  praainal  lines, 
which  serve  aa  guides  to  the  minor  details  of  the  drawing. 

■  Gothic  arrhitecture  that  we  meet  with  the  more  Burner- 
aai  a;  • .  ati  m  :'  aad  aaaf  n  •■:  : .  <;.  -  ::■  >  ;  .:«v!  aaalai  xr.J 
inea,  and  we  give  a  few  trample*  of  this  order  ia  Plate  IT. 
Fig.  5  repreaeau  the  upper  portion  of  a  window,  ccanpooed  of  a 
aerie*  of  area,  combed  ao  aa  to  form  what  are  denominated  ewepaf 
The  width  or  apaa.  A  a.  being  git  en.  aad  the  apex,  c . 
i .  draw  the  bisecting  perpendiculars,  cutting  a  >  in 
p  and  r_  Theae  Utter  are  the  centre*  of  the  sundry  concentric 
arcs.  mh..-h.  Ktrrally  rutting  each  other  oa  the  TerticaL  c  r.  form 
the  arch  of  the  window.  The  small  interior  eaapi 
in  the  same  manner,  aa  indicated  ia  the  figure ;  t 
c  B.  being  git  en.  also  the  apaa  aad  apnea.  Theae  mterior  archee 
are  manuana  sumvunied  by  the  nranarat.  a,  termed  aa  «a(-ew> 
•as/.  rniwwatiag  •imply  of  concentrk  rirrle*. 

tscoU  a  rowrtte,  f orated  by  cone 
the  outer  intrrsta-.es  containing  a  series  of  smaller  circlra.  fa 
an  interlaced  fillet  or  ribbon.  The  radio*.  A  o,  of  the  circle,  coa- 
taining  the  orotres  of  all  the  wnall  circles,  is  •apposed  lobe  given. 
amber  of  equal  parta.  With  the  poiata  of 
ditision.  1.  i  X  Ac  aa  centres,  deaeribe  the  cocbm  tangeataal  la 


BOOK    OF   INDUSTRIAL   DESIGN. 


each  other,  forming  the  fillet,  making  the  ra.lii  of  the  alternate 
ones  in  anv  proportion  to  each  other.  Then,  with  the  centre,  0, 
describe  concentric  circles,  tangential  to  the  larger  of  the  fillet 
circles  of  the  radius,  A  b.  The  central  ornament  is  formed  by 
arcs  of  circles,  tangential  to  the  radii,  drawn  to  the  centres  of  the 
fillet  circles,  their  convexities  being  towards  the  centre,  o:  and  the 
arcs,  joining  the  extremities  of  tfae  radii,  are  drawn  with  the  actual 
centres  of  the  fillet  circles. 

46.  Fig.  6  represents  a  quadrant  of  a  Gothic  rosette,  distin- 
guished as  radiating.  It  is  formed  by  a  series  of  cuspid  arches  and 
radiating  mulliuns.  In  the  figure  are  indicated  tie'  centra  lines  of 
the  seven]  arches  and  mullions.  and  in  fig.  6',  the  capital,  con- 
electing  the  niullion  to  the  arch,  is  represented  drawn  to  dottble 
the  scale.  With  the  given  radii,  a  b,  a  r,  a  d,  a  e,  describe  the 
different  quadrants,  and  divide  each  into  eight  equal  parts,  thus 
obtaining  the  centres  for  the  trefoil  and  quadrefoii  ornaments  in 
and  between  the  different  arches.  We  have  drawn  these  orna- 
ments to  a  larger  scale,  in  figs.  t>>,  t;>',  atui  6°,  in  which  are  indi- 
cated the  several  operations  required. 

47.  Fig.  4  also  represents  a  rosette,  composed  of  cuspid  arches 
and  trefoil  and  quadrefoii  ornaments,  but  disposed  in  a  different 
manner.     The  operations  are  so  similar  to  those  just  considered, 

that  it  is  unnecessary  to  enter  into  further  details. 

48.  Fig.  7  represents  a  cast-iron  grating,  ornamented  with 
Gothic  devices.  Fig.  7*  is  a  portion  of  the  details  on  a  larger 
scale,  from  which  it  will  be  seen  that  the  entire  pattern  is  made 
up  dimply  of  arcs,  straight   lines,  and  sweeps  formed  of  Ihese  two. 

the   problems  arising  comprehending  the  division   of  lines  aid 

angles,  and  the  iibtainment  of  the  various  centres. 

49.  Figs.  2  and  3  are  sections  of  tail-pieces,  such  as  are  sus- 
pended, as  it  were,  from  the  centres  of  Gothic  vimlts.  They  also 
represent  sections  of  certain  Gothic  columns,  met  with  in  the 
architecture  •if  the  twelfth  and  thirteenth  centuries.  In  order  to 
draw  them,  it  is  merely  necessary  to  determine  the  radii  and  centres 
of  the  various  arcs  composing  them. 

Several  of  the  figures  in  Plate  IV.  are  partially  shaded,  to 
indicate  the  degree  of  relief  of  the  various  portion*.      \\'e  have  in 

this  plate  endeavoured  to  collect  a  few  of  the  minor  difficulties, 

our  object  being  to  familiarize  the  student  to  the  use  of  his  instru- 
ment*, espi  eiallj  the  compasses.  These  exercises  will,  at  the  same 
time,  qualify  him  for  the  representation  of  a  vast  number  of  forms 
met  with  in  machinery  and  architecture. 


OVALS,  ELLIPSES,  PARABOLAS,  VOLUTES,  dec 

TLATE  V. 
50.  The  ore  is  an  ornament  of  the  shape  "I  an  egg,  and  is 
formed  of  arcs  of  circles.  It  is  frequently  employed  in  architecture, 
and  is  thus  drawn: — The  axes,  a  b  and  c  D,  fig.  1,  being  given, 
Perpendicular  to  each  other;  with  the  point  of  intersection,  o,  as  a 
centre.  tirst  describe  the  circle,  cade,  half  of  which  forms  the 
upper  portion  of  the  ove.  Joining  no,  make  it  equal  to  BE, 
the  difference  between  the  radii,  o  c,  o  b.  Bisect  F  B  by  the  per- 
pendicular. G  II.  cutting  c  D  in  H.  rt  will  be  the  centre,  and  II  c 
the  radius  of  the  arc.  c  I ;  and  i,  the  point  of  intersection  of  HC 
with  a  B,  will  be  the  centre,  ant!  I  B  the  radius  of  the  smaller  arc, 


I  B  K,  which,  together  with  the  arc,  II  K,  described  with  the  centre. 
I.,  and  radius,  id,  equal  to  lie,  form  the  lower  portion  of  the 
required  figure  ;  the  lines,  G  H,  L  K,  which  pass  through  the 
respective   e,  litres,  also   cut   the    arcs  in   the    points   of  junction. 

J  and  K.      This  ove  will    he  found  in    the    fragment    of  a   ei e, 

fig-  A-     A  more  accurate  and  beautiful   ove   may  be  dm  ami  by 
rf  the  instrument  represented  in  elevation  and  plan  in  the 
annexed  engraving. 


The  pencil  is  at  a,  in  an  adjustable  holder,  capable  of  sliding 
along  the  connecting-rod,  b,  one  end  of  which  is  jointed  at  c,  to  a 
slider  on  the  horizontal  bar,  D,  whilst  the  opposite  end  is  similarly 
joint,  il  to  the  crank  arm.  e.  revolving  on  the  fixed  centre,  F,  on 
tin  'oar.  By  altering  the  length  of  the  crank,  and  the  position  of 
the  pencil  on  the  connecting-rod,  the  shape  and  size  of  the  ovn 
may  '  •<  varied  as  required. 

51.  The  oral  differs  from  the  ove  in  having  the  upper  portion 
symmetrical  with  the  lower;  and  to  draw  it.  it  is  only  nec<  ssarv  to 
repeal  the  operations  gone  through  in  obtaining  the  curve,  l  b  f 
fig.  1. 

52.  The  ellipse  is  a  figure  which  possesses  the  following  pro- 
perty : — The  sum  of  the  distances  from  any  point,  a,  fig.  2,  in  the 
circumference,  to  two  constant  points,  n,  c,  in  the  longer  axis,  is 
alu.-,ys  equal  to  that  axis,  he,  The  two  points,  b,  i  -  are  b  mied 
foci.     The  curvi  forming  the  ellipse  is  i  ymmetrir  witf    referenci 

botU  to  the  horizontal  line  or  axis.  D  E,  and  to  the  vertical  line,  F  O. 
bisecting   the    former  in    0,    the   centre    of  the    ellipse.      Lines,  as 

B  a,  c  a,  b t,  c  f,  &c.,  joining  anj  point  in  the  circumference  with 
the  foci,  B  and  c,  are  called  vectors,  and  any  pair  proceeding  from 
one  point  are  togi  ther  equal  to  the  longer  axis,  d  e.  which  is  called 
the  fransreri  .  po  being  the  conjugate  axis.    There  are  different 

methods    of   drawing    this    curve,    which    we    will    proceed   to  in 

dicate. 

53.  First  Method. — This  is  based  on  the  definition  given  above, 

and   requires   that    the   two  axes   be   given,  as   he   and  F  G,  fig.  3. 

Tie  foci,  b  and  c,  are  tir-t  obtained  by  describing  an  arc,  with  the 

extremity.  G  or  F,  of  the  conjugate  axis  as  a  centre,  and  with  a 
radius,  fc,  equal  to  half  the  transverse  axis;  the  an  will  cut  tho 
latter  in  the  points,  r.  and  r.  the  foci.  If  now  we  divide  D  E 
unequally  iu  M.  and  with  the  radii,  n  H,  E  II.  and  the  foci  as  centr- -a, 
we  describe  ares  severally  cutting  each  (■ther  in  i.  j,  k.  a  ;  tin  « 
four  points  will  lie  in  the  circumference.  If,  further,  wo  agdB 
unequally  divide  d  e.  say  in  l,  we  can  similarly  obtain  four  ot  lei 


M 


Tllr'.  M  \VS 


poteta  in  the  rinrutnfrrt oc  and  we  ran.  in  Ekr  manner,  ..(tain  any 
number  of  p>4aU,  when  the  eifipae  mar  1- 
•  h%  hand.     Tne  Ur,->  etHpara  which  are  sometimes  required  in  eoo- 
atrarojooa,  are  generally  draw  a  with  a  tmmmrl  instead  of  com  paw, 
the   trammH    being   ■  ■    :h    adjustal... 

gmltmr'i  tUtpr:   To  ubtain  this,  place  a  rod  in  each  ol 
of  the  required  ellipse;  round  theae  place  an  endleiw  cord 
when  stretched  by  a  tracer. 
wiD  be  drawn   hj   es 

*»  4  b,  and  on  half  the 

|QaJ  to  half  ll 
v.l       Place    til.  -    so    tlial    ill. 

longer  meaaurvm«nt.  r  point, 

Daa   transverse  axis,  DC     I: 

axes — :  a  point 

in   the  circumference   which   may   be   narked   »itl>  a    |»  n.il.   the 
ellipae  being  alVrwanU  traced  throagfa  the  pointi  tint—  nbt 
55.    Third  MrthitL 

genHM-tr. 

:i  will   Iw  >n  My  lliat 

the  pr. 

being  given,  as  a  B  and  c  i>.  lh<  r  in   tin-  . 

draw  ao; 

11,111  dial 
1  n.  an.!  ' 

•    •  "1 

'. 
the   semicircle,  and.  :.' 
a  a,  «■•• 
equal  t. 
' 

iili   the 
- 

i.       Draw   radii,  cut) 

'V    that 
the  radii   ahould  !»•  al 

the  latter 
a  n.  nn.l  throagfa  the 
I 
■ 

which    may.    .  traced    throogil    tli.  m       It 

■  I  a  point  in  tl  I     • 

mint  a 

A  a.  and 

'j  in  j  ;  j.hd  ;  u  i»:  vflj  rut  rj    in  /     0/  will  be 


equal  U 

.  -  raar.  having 
the  ami 

. 
half  th. 

1  with  the  eonv 

ubtain 

I  lw>  seen  that 

:.rca  of  circle*, 

and  that  thoe  Jarl*  an  -    and  by 

-  axia  ia 
drawn 
nln,  the 

: 

but  witii  onlj 

'liout,  but    tlio 

must  alwaya  1«    within,  ami.  i 
■  r  be  a  ithoul 

•  all  poa- 

ii  and  n..t  to 

■ 

be  tli" 

I 

li..n  ;  ami  al-".  that  it  "  """l  '"'l  lo 

another,  it  en 

Lei  i 
both  in  '  »»d  ■,  and  make  a  r  equal 

•     i    draw    I  ll   parallel  to  C  a. 


1   ii  I.  a  J.  and  c  t\  equal  to  it  G  :  J'in  i  x.  and  baaaSl  it  in  a, 
ami  at  i  DxateuaW,  eottBf,  I  Pi  Of  I  D  pTOlfonad,  at  at; 

-  of  the 

!  .ii    M  !<   and  I  ra«iii  of 

tin-  pointi  U  cntart 
-.  drawn  thr- 
ipse. 


BOOK  OF  INDUSTRIAL  DESIGN. 


Several  instruments  have  been  invented  "for  drawing  ellipses, 
many  of  them  very  ingeniously  contrived.  The  best  known  of 
these  contrivances,  are  those  of  Farey,  Wilson,  and  I  lick — tho 
last  of  which  we  present  in  the  annexed  engraving:  It  is  shown 
as  in  working  order, 
with  a  pen  for  drawing 
ellipses  in  ink.  It  con- 
sists of  a  rectangular  base 
plate,  A,  having  sharp 
countersunk  points  on 
its  lower  surface,  to  hold 
the  instrument  steady, 
and  cut  out  to  leave  a 
Sufficient  area  of  tho 
paper  uncovered  for  the 
traverse  of  the  pen. 
It  is  adjusted  in  position 
by  four  index  lines, 
setting  out  the  trans- 
verse and  conjugate 
axes  of  the  intended 
ellipse  —  these  lines 
being  cut  on  the  inner 
edges  of  the  base.  Near 
»ne  end  of  the  latter,  a  vertical  pillar,  b,  is  screwed  down,  for  the 
purpose  of  carrying  the  traversing  slide-arm,  c,  adjustable  at  any 
height,  by  a  milled  head,  D,  the  spindle  of  which  carries  a  pinion 
in  gear  with  a  rack  on  the  outside  of  the  pillar.  The  outer  end 
of  the  ami,  c,  terminates  in  a  ring,  with  a  universal  joint,  e, 
through  which  the  pen  or  pencil-holder,  F,  is  passed.  The  pillar, 
B,  also  carries  at  its  upper  end  a  fixed  arm,  g,  formed  as  an  ellip- 
tical guide-frame,  being  accurately  cut  out  to  an  elliptical  figure,  as 
the  nucleus*  of  all  the  varieties  of  ellipse  to  be  drawn.  The  centre 
of  this  ellipse  is,  of  course,  set  directly  over  the  centre  of  the 
universal  joint,  E,  and  the  pen-holder  is  passed  through  the  guide 
aud  through  the  joint,  the  fiat-sided  sliding-piece,  h,  being  kept  in 
contact  with  the  guide,  in  traversing  the  pen  over  the  paper.  Tho 
pen  thus  turns  upon  its  joint,  E,  as  a  centre,  and  is  always  held  in 
its  proper  line  of  motion  by  the  action  of  the  slider,  h.  The  dis- 
tance between  the  guide  ellipse  and  the  universal  joint  determines 
the  size  of  the  ellipse,  which,  in  the  instrument  here  delineated, 
ranges  from  2J  inches  by  1J,  to  jg  by  \  inch.  In  general,  how- 
ever, these  instruments  do  not  appear  to  be  sufficiently  simple,  or 
convenient,  to  be  used  with  advantage  in  geometrical  drawing. 

57.  Tangents  to  ellipses. — It  is  frequently  necessary  to  deter- 
mine the  position  and  inclination  of  a  straight  line  which  shall 
be  a  tangent  to  an  elliptic  curve.  Three  cases  of  this  nature 
occur :  when  a  point  in  the  ellipse  is  given  ;  when  some  external 
point  is  given  apart  from  the  ellipse  ;  and  when  a  straight  lino 
is  given,  to  which  it  is  necessary  that  the  tangent  should  bo 
parallel. 

First,  then,  let  the  point,  A,  in  the  ellipse,  fig.  2,  be  given  ; 
draw  the  two  vectors,  c  A,  B  A,  and  produce  the  latter  to  M";  bisect 
the  angle,  mac,  by  the  straight  line,  N  p ;  this  line,  it  p,  will  be 
'vie  tangent  required;  that  is,  it  will  touch  the  curve  in  the  point, 
A,  and  in  that  point  alone. 


Secondly,  let  the  point,  i,  be  given,  apart  from  thjs  elli 
3.     Join  l  with  i,  the  nearest  focus  to  it,  and  with  i.  as  ,,  . 

and  a  radius  equal  to  i.  i,  describe  an  are,  si  I  >'.  Next,  with  tho 
more  distant  focus,  h,  as  a  centre,  and  with  a  radius  equal  in  the 
transverse  axis,  a  b,  describe  a  second  arc,  cutting  the  first  in  h 
ami  n.    Join  m  h  and  n  ii,  and  the  ellipse  will  be  cul  iii  ill' 

r  and  ,c;  a  straight  line  drawn  through  either  of  these  points  from 
the  given  point,  L,  will  be  a  tangent  t"  tli.-  ellipse. 

58.  Thirdly,  lei  the  straight  fine,  q  r,  fig.  2,  be  given,  parallo 
to  which  it  is  required  to  draw  a  tangent  to  the  ellip.-o.  From  the 
nearest  focus,  b,  let  fall  on  q  H  the  perpendicular,  s  b;  then  with 
the  further  focus,  c,  as  a  centre,  and  with  a  radius  equal  to  tho 
transverse  axis,  d  e,  describe  an  arc  cutting  b  s  in  s :  join  I  -.  and 
the  straight  line,  c  s,  will  cut  the  ellipse  in  the  point,  T.  of  contact 
of  the  required  tangent.  All  that  is  then  necessary  is,  to  draw 
through  that  point  a  line  parallel  to  the  given  line,  ij  r,  tho 
accuracy  of  which  may  be  verified  by  observing  whether  ii  I' 
the  line,  s  b,  which  it  should. 

59. — The  oval  of  fine  centres,  fig.  4. — As  in  previous  cases,  the 
transverse  and  conjugate  axes  are  given,  and  we  commence  by 
obtaining  a  mean  proportional  between  their  halves;  for  this 
purpose,  with  the  centre,  o,  and  the  semi-conjugate  axis,  o  c,  as 
radius,  we  describe  the  arc,  c  I  K,  and  then  the  semi-circle,  a  l  k,  of 
which  A  K  is  the  diameter,  and  further  prolong  o  c  to  i.,  0  l  being 
the  mean  proportional  required.  Next  construct  the  parallelo- 
gram, a  g  c  o,  the  semi-axes  constituting  its  dimensions;  joining 
c  A,  let  fall  from  the  point,  G,  on  the  diagonal,  c  a,  the  per- 
pendicular, g  ii  d — which,  being  prolonged,  cuts  the  conjugate  axis 
or  its  continuation  in  D.  Having  made  c  M  equal  to  the  mean 
proportional,  o  i„  with  the  centre,  n,  and  radius,  u  M,  describe 
an  arc,  a  U  Ii ;  and  having  also  made  a  n  equal  to  the  mean  pro- 
portional, 0  L,  with  the  centre,  Ii,  and  radius,  n  \.  describe  tie 
arc,  n  a,  cutting  the  former  in  a.  The  points,  n.  ti,  on  01 
and  n',  b,  obtained  in  a  similar  manner  on  the  other,  to)  i  thi  r 
with  the  point,  D,  will  be  the  five  centres  of  the  oval  :  and  1 

lines,  R  H  a,  s  h'  b,  and  p  a  D,  q  b  D,  passing  through  the  r.    ; 
centres,  will  meet  the  curve  in  the  points  of  junction  of  the  various 
oomponent  arcs,  as  at  R,  P,  q,  s. 

This  beautiful  curve  is  adopted  in  the  construction  of  many 
kinds  of  arches,  bridges,  ami  vaulls  :  an  example  of  its  use  is  _i\.  n 
in  fig.  ©. 

60.  The  parabola,  fig.  5,  is  an  open  curve,  that  is.  one  which 
does  not  return   to  any  assumed   starting  point,  to  how. 

a  length  it  may  be  extended;  and  which,  consequently,  can  nevei 
enclose  a  space.  It  is  so  constituted,  that  any  point  in  it,  d,  is  at 
an  equal  distance  from  a  constant  point.  .  .  termed  the  focus,  and 
in  a  perpendicular  direction,  from  a  straight  line,  a  k.  cal 
directrix.  The  straight  line,  F  G,  perpendicular  to  the  directrix, 
A  B,  and  passing  through  the  focus,  c,  IS  the  axis  of  the  curve, 
which  it  divides  into  two  symmetrical  portions.  The  point.  A, 
midway  between   F  and  r,  is  the  apex   of  the  curve.      Thi 

several  methods  of  drawing  thi-  curve. 

61.  First  method: — This  is  based  on  the  definition  jusl 

and  requires  that  the  focus  and  directrix  be  known,  as  e.  and  a  p. 
Take  any  points  on  thi'  directrix,  A  B,  as  a.  e,  II.  I.  and  thronin 
them  draw  parallels  to  the  axis,  f  g,  as  also    the  straight   linen 


niii:  1 


i 

■•ui.n„»  para! 
.kill  be  in  the 

nam 

:    drawn,   cu! 

■ 
I 

■taking  h  c  equal  to  e  c,  ati 

I 
. 

■ 

.  lit  Tail 

puts,  as 

I'.irall.-N  tn   :' 
• 

r..m  the 
m,  n,  ii, 

parabola, 

•ad  pnr  D    Bna,  J  K,  we   let   fall   a  [n  riiendieular,  C  L, 

drawn  parallel  I  cut  the  cam  in  tin-  tN.in- 

tact,  n. 

• 

-■ 

'  iple  of 
I  /' 

and   ar> 

-   from  llii-  pnu 
"f   oue  tnirp.r,  b  /,  Ibj   Sat 

)-.  a*,  ..!' 

' 

lane*  apart;  fur  all  t!i  |„.  ulnar,  J/J 

-.  nnd  arc  nir-. 

•        /  /  • 

rammit  to  ili 
.  il    parte,  ninl  with  ll,. 

I- 
1 

!  nnd  4 — 2,  pan 

I 

•  t.,  the 
J      With  ihi-. 

I  ■  i 


i  a  lirw 
drawn 
radian,  1'  a',  a  I 

. —  liiill 

!' 

carta.    J 

and/'  will  he  uthir  t. 

» 
In-  mil  with  in 

feet  a  c 


s  ,\\l)  PRACTICAL  DATA 
i.  i  a  ii 

• 

rut  the  111 

dhridod  into  tbi 

\  ■ 

■ 

m  uail- 

■ 
In  the  aune  manner  ! 

■ 
And    tli- 
for, 

■ 
It  in  in   ' 
■ 

0)    i»  the  iiin: 
a  square  raid.  ;  for 

4  1  foot  as  \  yard  X  {  yn.nl  -  J  wjiiu 

A  •v|n.'«T  inch  i'  the  i  nth  part  of  ■ 

.  fur 

I  Inch  x  I  men      ,'.  fool  >  toot, 

nnd 

1  men  x  1  Inch  —  ,',  \nnl  > 
Thi*  Diustral  ■  t   lha 

of  other  methoda, 

■  nr  an  a  "f  ■ 
ea  and  | 
;  llano  ur  length,  and 


BOOK  OF   INDUSTRUL  DES1UN. 


perpendicularly  from  the  base.  Thus  the  area  of  a  rectangle,  the 
base  of  which  measures  1-25  metres,  and  the  height  -75,  is  equal  to 
1-25  x  -75  =  -9375  square  metres. 
The  area  of  a  rectangle  being  known,  and  one  of  its  dimensions, 
the  other  mav  be  obtained  by  dividing  the  area  by  the  given, 
dimension. 

Example. — The  area  of  a  rectangle  being  -9375  sq.  m.,  and  the 
base  125  m.,  the  height  is 

=:  -7o  m. 

l-as 

-This  operation  is  constantly  needed  in  actual  construction  ;  as,  for 
instance,  when  it  is  necessary  to  make  a  rectangular  aperture  of  a 
certain  area,  one  of  the  dimensions  being  predetermined. 

The  area  of  a  trapezium  is  equal  to  the  product  of  half  the  sum 
of  the  parallel  sides  into  the  perpendicular  breadth. 

Example. — The  parallel  sides  ot  a  trapezium  being  respectively 

1-3  in.,  and  1-5  in.,  and  the  breadth  -8  m.,  the  area  will  be 

1-3  +  15       „ 

^ x  -8  =  1-12  sq.  m. 

The  area  of  a  triangle  is  obtained  by  multiplying  the  base  by 
half  the  perpendicular  height. 

Example. — -The  base  of  a  triangle  being  23  in.,  and  the  perpen- 
dicular height  1-15  m.,  the  area  will  be 


23   x 


115 

2 


13225  sq.  m. 


The  area  of  a  triangle  being  known,  and  one  of  tlft  dimensions 
given — that  is,  the  base  or  the  perpendicular  height — the  other 
dimension  can  be  ascertained  by  dividing  double  the  area  by  the 
given  dimension.  Thus,  in  the  above  example,  the  division  of 
(1-3225  sq.  in.  x  2)  by  the  height  1-15  m.  gives  for  quotient  the  base 
2-3  m..  and  its  division  by  the  base  2-3  m.  gives  the  height  1-15  m. 

70.  It  is  demonstrated  in  geometry,  that  the  square  of  the 
hypothenuse,  or  longest  side  of  a  right-angled  triangle,  is  equal  to 


the  sum  of  the  squares  of  the  two  sides  forming  the  right  angle. 
It  follows  from  this  property,  that  if  any  two  of  the  sides  of  a 
right-angled  triangle  be  given,  the  third  may  be  at  onei  ascertained. 

First,  If  the  sidos  forming  the  right  angle  be  given,  the  hypo. 
thenuse  is  determined  by  adding  together  their  squares,  ami 
extracting  the  square  root. 

Example.— The  side,  A  B,  of  the  triangle,  a  b  C,  tig.   Hi,  II.  I., 
being  3  in.,  tho  side  B  c,  4  m.,  the  hypothenuse,  A  e,  will  be 
A  c  =  l/3a+4-  =    V'y  +  16  =  1/25  =  5  m. 

Secondly,  If  tho  hypothenuse,.  as  a  c,  be  known,  and  one  of 
the  other  sides,  as  a  b,  the  third  side,  B  c,  will  be  equal  to  tho 
square  root  of  the  difference  between  the  squares  of  a  c  and  A  B. 

Thus  assuming  the  above  measures — 


Be  =   V25  — 9  =  Vl6  =  4  m. 

The  diagonal  of  a  square  is  always  equal  to  one  of  the  sides  mul 
tiplied  by  y-2;  therefore,  as  Vi  =  1-414  nearly,  the  diagonal  is 
obtained  by  multiplying  a  side  by  1-414. 

Example. — The  side  of  a  square  being  6  metres,  its  diagonal 
=  6  X  1-414  =  8-484  m. 
The  sum  of  the  squares  of  the  four  sides  of  a  parallelogram  is 
equal  to  the  sum  of  the  squares  of  its  diagonals. 

71.  Regular  polygons. — The  area  of  a  regular  polygon  is 
obtained  by  multiplying  its  perimeter  by  half  the  apothegm  or  pet 
pendicular,  let  fall  from  the  centre  to  one  of  the  sides. 

A  regular  polygon  of  5  sides,  one  of  which  is  9-8  m.,  and  the 
perpendicular  distance  from  the  centre  to  one  of  the  sides  5-t;  in., 
will  have  for  area — 

9-8  x  5  x  51=  137-2  sq.  in. 
The  area  of  an  irregular  polygon  will  be  obtained  by  dividing  it 
into  triangles,  rectangles,  or  trapeziums,  and  then  adding  together 
the  areas  of  the  various  component  figures. 


TADLE  OF  MULTIPLIERS  FOR  REGULAR   POLYGONS  OF  FROM  3  TO  12  SIDES. 


Names. 

Sides. 

Multipliers. 

D 

Area 

.  1  side  =  1. 

E 

liil<  nutl  Angle. 

F 

Apothegm 

A 

B 

c 

Pi    I  i  ndicnlar. 

3 

4 
5 
6 
7 
8 
9 
10 
11 
12 

2-000 
1-414 
1-238 
1156 
1.111 
1-080 
1-062 
1-050 
1-040 
1-037 

1-730 
1-412 
1-174 

radius. 
•867 
•765 
•681 
•616 
•561 
•516 

•579 
•705 
•852 
side. 
1-160 
1-307 

1-470 

1-625 
1-777 
1-940 

•433 
1-000 
1-720 
2-598 
3-634 
4-828 
6-182 
7-694 
9-365 
11-196 

60°  0' 

90°  0' 
108°  0' 
120°  0' 
128°   3  1'  = 
135°   0' 
140°  0' 
144°  0' 
147°   16Vr 
150°  0' 

•l'nnoT.'jI 
■5000000 
■6881910 
■8660264 
1 '0382607 
1-2071069 
1-3737387 
1-5388418 
1-7028436 
1-8660234 

By  means  of  this  table,  we  can  easily  solve  many  interesting 
problems  connected  with  regular  polygons,  from  the  triangle  up  to 
the  duodecagon.     Such  are  the  following  : — 

First,  The  width  of  a  polygon  being  given,  to  find  the  radius  of 
the  circumscribing  circle. — When  the  number  of  sides  is  even,  the 
width  is  understood  as  the  perpendicular  distance  between  two 
opposite  and  parallel  sides;  when  the  number  is  uneven,  it  is 
twice  the  perpendicular  distance  from  the  centre  to  one  side. 


Rule. — Multiply  half  the  width  of  the  polygon  by  tin  factor,  in 

column  A,  corresponding  to  the  number  of  sides,  and  the  product 
will  be  the  required  radius.  * 

Example. — Let  18-5 m.  be  the  width  of  an  octagon;  then. 


18^5 
2 


x   1-08  =9-99  m.; 
or  say  10  metres,  the  rudius  of  the  circumscribing  circle. 


•.  7V  rasSai  «/  m  circle  krimg  gim.  to  fad  At  Itngm  tf 
tir  nsVo/  am  itucrikml  pttjgtm. 

ply  the   radio*  by   the  factor  in  column  B,  curre- 
sr*>odmf  to  the  number  of  •idea  of  tl>c  required  polygon. 

TIM  radius  bang  10  m,  the  side  of  an   inscribed 
..  ktj    -.  »...  U — 

"65  m. 
Third.  TV  naV  of  «  pcifgtm  being  gitta,  u>  find  Ike  radius  tf 
V*  citrvmuerikmg  circle. 

pij  the  side  by  thi 
•  number  of  aides. 
Exat  ii.  be  the  aide  of  an  octagon  ;  then 

:=  loo,  nearly. 
TV  rssV  if  a  polugtm  brtnt;  giren,  to  find  Ike  area. 

side   by  the   (actor   in   column    D, 
euneapuoding  to  the  number  of  airlea. 

I*. — The  aide  of  an  octagon  being  7-65  m.,  the  area  win 

I  828  =  36-93  >q.  m. 

Tlir  l    AtD    AKEA   OF    A   CIKCLE. 

.  diame- 
I*  a  numU  r  *otio  tf 

tie  ctmimftrcnce  to  Ike  diameter.     The  ratio  is  found  to  be  (ap- 
I 

3  1116.  or  -J.:     - 
that  is,  the  circumference  equals  31 4 16  time*  the 
raie>   formula*. 
- 
and  0  ili  dans  ula, 

- 

-.  if  the 
D  radius  II  =  1-35  m., 

the  circumference  will  be  equal  to— 

■ 

cir  „:..:.  :.  ;►  ■      f  »  s  8    i-J  ID  .  . 


and  the  radius,  R.  is — 


=  1  35  m. 


•  .-   - 

TV  arm  tf  a  circle  iiftmmd  bm  multiphfing  Ike  circumference  km 
kalf  ike  radiut. — This  rale  i»  expressed  in  the  following  formula : — 

The  ana  of  a  circle  =  i«Rxi  =  , 

i 

■•  rtn,  k  R*,  is  merely  the   simpmVatioej  of  the  formahv 
TV   number  U  U-in_-  ■  r  and   divisor,  may  be  can- 

celled, and  the  produ  .or  tha. 

square  of  the  radius.     It  follows,  then,  that  the  area  of  a  circle  is 
equal  to  the  square  of  the  radius  multiplied  by  the  cin-uiiifcrcnce, 

Example. — The  radius  of  a  circle  being  1-05  m..  the  area  win 
be— 

t-Mlfl  x   l  -j.  m. 

The  .-.-  .the  radius  is  determu>-d  by 

.  :he  area  by  3-1416,  and  extracting  the  square  ruot  of  tha 

Example. — The  area  of  a  circle  being  34635  sq.  m..  the  radios 


V 


The  area  of  a  circle  i-   . 

.              x  I> 
Area  = ,  or 


'.    - 


;D». 

•1     ' 


4 

That  ia  1  the  square  of 

the  diai:  :«■  the  area. 

Example. —  h  mea- 

m. 
■Iial  if  the  ana  of  a  Mjuare  is  l:..»n.  that 
of  an  inscribe-!  I;  that 

ia,  the  ana  of  a  sanan  i .  as, 

4  :  . 


TABLE    Of    ArTBOXIXATE     RATIOS    Bt7 


X 



X 

...  X 


.  (mQu- 

Lb*  side  of  a  square  of  equal  area  is 


14141 


»!  area. 
=      thr-  - 


Qg  860*/.,  the  aid*  of 

860  > 
TIM  *'•"•'..  the  diameter  of 

in  .  irBs»»assrJbta*j  ,•;-> '.   Ii 


BOOK  OF  INDUSTRIAL  DESIGN. 


Tin'  radii  and  diameters  of  circles  are  to  each  other  as  the  cir- 
cumferences, and  vice  versa.  The  areas,  therefore,  of  circles  are  to 
each  other  as  the  squares  of  their  respective  radii  or  diameters. 

It  follows,  hence,  that  if  the  radius  or  diameter  be  doubled,  the 
circumference  will  only  be  doubled,  but  the  area  will  be  quadrupled ; 
thus,  a  drawing  reduced  to  one-half  the  length,  and  half  the 
breadth,  only  occupies  a  quarter  of  the  area  of  that  from  which  it 
is  reduced. 

73.  Sectors — Segments. — In  order  to  obtain  the  area  of  a  sector 
or  segment,  it  is  necessary  to  know  the  length  of  the  arc  subtend- 
'  big  it.  This  is  found  by  multiplying  the  whole  circumference  by 
the  number  of  degrees  contained  in  the  arc,  and  dividing  by  360°. 

Example. — The  circumference  of  a  circle  being  3-5  in.,  an  arc  of 
4  0 '  will  be 

3-5  x  45 


360 


=  -4375  m. 


The  length  of  an  arc  may  be  obtained  approximately  when  the 

chord  is  known,  and  the  chord  of  half  the  arc,  by  subtracting  the 

chord  of  the  whole  arc  from  eight  times  the  chord  of  the  semi-arc, 

and  taking  a  third  of  the  remainder. 

Example. — The  chord  of  an  arc  being  -344  m.,  and  that  of  half 

the  arc  "198,  the  length  of  the  are  is 

•198  x  8— -344 

=    4133  m. 

3 

The  area  of  a  sector  is  equal  to  the  length  of  the  arc  multiplied 

into  half  the  radius. 


Example. — The  radius  being  -169  in.,  and  the  are  -_iiii; 

•266  x  -169        „,,.  ' 

=  -0225  sq.  m.,  the  area  ol  the  sector. 

The  area  of  a  segment  is  obtained  by  multiplying  the  width  ;  that 
is,  the  perpendicular  between  the  centre  of  the  chord,  and  tho 
centre  of  the  are,  by  -626,  then  adding  to  the  square  of  the  pro- 
duct the  square  of  half  the  chord,  and  multiplying  twice  the 
square  root  of  the  sum  by  two-thirds  of  the  width. 

Example.— let  48  in.  be  the  length  of  the  chord  of  the  are, 
and  18  in.  the  width  of  the  arc,  then  we  have 

18  x  -626  =  11-268,  and  (11-268)-'  =  126-9678;  whilst 

2x18 

:  576;  therefore, 2  x  V  126-9678  +  576  x  ——  =  630-24 

sq.  m.,  the  area  of  the  segment. 

The  area  of  a  segment  may  also  bo  obtained  very  approximately 
by  dividing  the  cube  of  tho  width  by  twice  the  length  of  the  chord, 
and  adding  to  tho  quotient  the  product  of  the  width  into  two 
tliirds  of  the  chord.     Thus,  with  the  foregoing  data,  we  have 


(?)' 


and, . 


=  576-0 


Total,  636-7  sq.  m. 

A  still  simpler  method,  is   to  obtain  the  area  of  the  sector  of 
which  the  segment  is  a  part,  and  then  subtract  the  area  of   the 


COMPARISON*  OF  CONTINENTAL  MEASURES,  WITH  FRENCH   MILLIMETRES  AND  ENGLISH  FEET. 


Value  in 

Value  in 

MiLhnielres. 

Feet. 

S16-103 

1-037 

296-416 

■970 

435-185 

1-460 

■■,;:■■■::■•■ 

1-140 

3  96  -500 

1-301 

300-000 

•984 

291-859 

•958 

296-168 

•972 

1,000-000 

3281 

285-588 

•937 

289-197 

•949 

285-362 

•936 

35(5-421 

1-169 

313-821 

1-029 

282-655 

•927 

635-906 

2742 

B47-965 

2-782 

297-896 

■977 

ti-j:;-422 

•733 

294-246 

■968 

284-610 

•933 

286-490 

•940 

291-995 

•958 

300-000 

•984 

Designation  of  Me 


Austria 

Baden, 

Bavaria,  .... 

Belgium 

Bremen, .... 

Brunswick,  . , 

Cracovia, 

Denmark, 

Spain, 

Papal  States,,  -j 

Frankfort 

Hamburg 

Hanover, , 

Hesse 


(Vienna)    Foot    or    Fuss    =    1 

inches  =  144  lines 

(Bohemia)  Foot, 

(Venice)  Foot, 

Foot  (Paliuo) 

"        Foot  (Architect's  Meas.) 
(Cai-lsruhe)    Foot    (new)    =    10 

inches  =  100  lines 

(Munich)  Foot  =  12  inches  = 

144  lines, 

(Augsburg)  F"oot 

(Brussels)  Ell  or  Aline  =  1  metre, 

Foot, 

(Bremen)  Foot  =  12  inches  = 

144  lines, 

(Brunswick)  Foot   =  12  inche 

=  144  lines 

(Cracow)  Foot, 

( Copenhagen)  Foot 

(Mini  rid)  Foot  (according  to  Loh 


Castilian  Vara  (       "         Liscar), 
(Havana)  Yara=  3  Madrid  feet. 

(Pome)  Foot 

Architect's  Span  =  *  foot, 

Ancient  F'oot 

Pool 

Foot  =  3  spans  =  12  inches  = 

96  parts 

(Hanover)  Foot  =  12  inches  = 

144  lines, 

(Darmstadt) Foot  =  lo  inches 

100  lines, 


Lubeck, . . 
Mecklenburg, 

Modena,. 


(Amsterdam)  Foot 

|     =11  inches 

(Rhine)  Foot 

( Lubeck)  Fout,. . . . 


3    spans 


I 

I 

Ottoman  Enipin 
Parma 

Poland 


Portugal, . 

Prussia,.  .  . 

Russia, . . . 

Sardinia,.  . 
•Saxc 

Sicilies,. . . 


Switzerland,  . 


Tuscany, 

Wui-temburg,.. 


I  oot, 

(Modena j  Foot, 



I I  onstantinople)  Grand  |  u . 
Anns-length  =  12  inches  =  172s 

atoini 

(  Varsox  ie)  Foot  =  12  inches 

144  lines 

(Lisbon)  Ft.  (ArchitecfsMeasure) 

"        Vara  =  40  inches 

(Berlin)  Foot  =  12  inches 

(St.  Petersburg)  Russian  Foot; 

"  Archine 

(Cagliari)  Span, 

(  Weimar)  Foot 

Span  =  12  inches  (ounces  =  6o 

niinuti) 

(Stockholm)  Foot, 

i  Bale  and  Zurich)  Foot 

(Berne  and  Neufchatel)  Fool   - 

•i  inches 

(Geneva)  Foot 

i  Lausanne)  Foot  =  10  inches  = 

100  lines 

(Lucerne  and  other  Cantons)  Ft.. 

Foot, 


Foot  =  10  inches  =  100 


813864 

623-048 

66S  I  , 

oil  670 

297-769 

388-6 

1,008-868 
309-726 

711-480 
202-678 
281-97J 

268-670 


1-080 

i 
1-718 
1-742 
2-196 

1787 


1-111 

1-766 
2-884 

■60  l 

.-865 

•97  1 
•999 

■962 
1-600 

■984 

1-O30 


• 


■ 


J  the  area  of  an  annular  space  contain.  <: 
•MMBtrie  rirvi.-*,  multiply  the  »um  of  iho  duu. 
dil!«rroc< ,  and 

100  -f  60)  X  (1  '"•  Iho 

'    tha  annular  (face. 
TV»  arcs  ul  annular  apace 

needy,  by  tin-  are  which  is  a  niraii  |irop.,rtiiinal  to  .. 
Un    AREA  OF    AX    (LI.:. 

n  U  equal  to  I 
of  wtikh  the  diameter  ia  a  mean  proportional  between  Ibe  tn 


■ 

Uonal  by 

- 
tiff  u 

i 
The  arrsa  of 

'  :  and  tho 
-   area  ol 

/  |      • 

truil  arU,  an. I   |«rticiilarly   i\ 

Oft     The  ejBJ  | 

^,   as   well    ea  -. 

problem.-.. 


CHAPTER  II. 
THE   STUDY   OF   PROJECTIONS. 


>  all  the  dimensions  of  an  • 
■ 

mprehended  under  the 
of  P 
and  aa  I  lone,  or 

lion  "!i  papi  r  of  the  appear- 
i  from  diflerant 

■  a  body  on  two 
principal  plain*,  ••:.«■  of  which  is  distinguished  as  Ibe  horizontal 
plant,  and  the  I 

planes  are  alan  Thoj  an' 

h  other,  tho  horizontal  plan  In  ■in;;  the  lower;  Ibe 
d  the  Ixise  li/ir,  and  i- 
to  one  l  : 

.i  thorough  Imowli  dge  of  tin' 
-. .  in  order  to  In'  able 
terminate  forma,  the  eontotui 
1  now  i  nter  npon  tn  h  up 
u  axe  Meeaaarj  primarily  with  Ibe  projectiona 

of  a  potet  and  Of 


[ENTARY  PRINCIPLES 
.    tiii:  rBojBOTtoaa  or  a  poikt. 

I'l.MK    VI. 

■    l  and  f,  !«•  ■  horlsontaj  : 
ird  on   which  Ui-  dri 
made,  or  parhaj  let  a  n  e  r  bo 

plane.  Meg  at  a  wall  at  one  side  of  tin 
in-  nt ,    the   »trai(fht   I 


r         '  ■  .. 

of  which  it  i-  ■ 

i  perpendicular,  o  o,  to  !>>•  Icl  fail  on  the  l- 
plane,  Dm  pohrl  ndicoJar, 

will  be  what  is  mid.  i  .  ..f  the 

given  point    Similarly,  If  from  ibe  point,  o,  we  • 
pendictil  i,  tho 

point  ol  or  fool  of  ti  •  ar,  will   be  th« 

vertioal  projection  "i  the  tame  point    TI  Jim  are 

■  d   in   the  Vertical  and  borixo 

6  n  and  .   |uir;i]!rl  and  eipial  I 

".    Il    follow!  .ii-truetii in,  that,  when   the   I 

of  any  point  are  given,  the  position  in  spa*  I 

■  letertninalile,  it  being  necessarily  the  |>"int 

of  narpendieul  of  the 

point 

A*  in  dm* 
of  paper,  and  ■ 
plane,  it  la  customary  t"  rapp 
ils  forming  a  eontinnation  of  the  ho 

turned  on  the  baM  On  ith  il — ■ 

il.it  mi  a  labli      \\  i 
thua  obtain  tie 

tin-  two  lad  b]  the  base  line,  a  b,  and 

the  poinl 

of  the  given  |K,int. 

It  will  l»'  remarked,  thai  these  pointa  1" 
(li.-ular  lo  the   b  ■  .  in  the  turnine;  down 

Of  the  previously  verticil  plane,  the   | 
t i. .ii  of  Ihe  line,  n  0.      It  is  I!cvo>-siry  to  obasfTa,  that  tin 

poinl   from  the   horizontal   plane, 
whilst    n   a   measures 

other  sjnras,  if  on  ■  m  arjaot  a  nsfnaadaNlai  kg  la*  plane,  and 


BOOK  OF  INDUSTRIAL  DESIGN. 


measure  the  distance,  n  o',  on  this  perpendicular,  we  shall  obtain 
the  exact  position  of  the  point  in  space.  It  is  thus  obvious,  that 
the  position  of  a  point  in  space  is  fully  determinable  by  means  of 
two  projections,  these  being  in  planes  at  right  angles  to  each 
other. 

THE    PROJECTIONS   OF   A   STRAIGHT   LINE. 

78.  In  general,  if,  from  several  points  in  the  given  line,  perpen- 
diculars be  let  fall  on  to  each  of  the  planes  of  projection,  and 
their  points  of  contact  with  these  planes  be  joined,  the  resulting 
lines  will  be  the  respective  projections  of  the  given  line. 

.  When  the  line  is  straight,  it  will  be  sufficient  to  find  the  pro- 
jections of  its  extreme  points,  and  then  join  these  respectively  by 
straight  lines. 

79.  Let  M  o,  fig.  2,  represent  a  given  straight  line  in  space, 
which  we  shall  suppose  to  be,  in  this  instance,  perpendicular  to 
the  horizontal,  and,  consequently,  parallel  to  the  vertical  plane  of 
projection.  To  obtain  its  projection  on  the  latter,  perpendiculars, 
M  m',  o  o',  must  bo  let  fall  from  its  extremities,  m,  o  ;  the  straight 
line,  w!  o',  joining  the  extremities  of  these  perpendiculars,  will  be 
the  required  projection  in  the  vertical  plane,  and  in  the  present 
case  it  will  be  equal  to  the  given  line. 

The  horizontal  projection  of  the  given  line,  M  o,  is  a  mere 
point,  m,  because  the  line  lies  wholly  in  a  perpendicular,  M  m,  to 
the  plane,  and  it  is  the  point  of  contact  of  this  line  which  consti- 
tutes the  projection.  In  drawing,  when  the  two  planes  are 
converted  into  one,  as  indicated  in  fig.  2°,  the  horizontal  and  ver- 
tical projections  of  the  given  right  lines,  in  o,  are  respectively  the 
point,  m,  and  the  right  line,  m'  u'. 

80.  If  we  suppose  that  the  given  straight  line,  M  o,  is  horizon- 
tal, and  at  the  same  time  perpendicular  to  the  vertical  plane,  as 
in  figs.  3  and  3%  the  projections  will  be  similar  to  the  last,  but 
transposed;  that  is,  the  point,  e/,  will  be  the  vertical,  whilst  the 
straight  line,  m  o,  will  be  the  horizontal  projection. 

In  both  the  preceding  cases,  the  projections  lie  in  the  same 
perpendicular  line,  m  m,  fig.  2",  and  o'  o.  fig.  5". 

81.  When  the  given  straight  line,  M  o,  is  parallel  to  both  the 
horizontal  and  the  vertical  plane,  as  in  figs.  4  and  4",  its  two  pro- 
jections, m  o  and  ?n'  o',  will  be  parallel  to  the  base  Hue,  and  they 
will  each  be  equal  to  the  given  line. 

82.  When  the  given  straight  line,  M  o,  figs.  5  and  5",  is  parallel 
to  the  vertical  plane,  abef,  only,  the  vertical  projection,  m  o', 
will  be  parallel  to  the  given  line,  whilst  the  horizontal  projection, 
m  y,  will  be  parallel  to  the  base  line.  Inversely,  if  the  given  straight 
line  be  parallel  to  the  horizontal  plane,  its  horizontal  projection  will 
be  parallel  to  it,  whilst  its  vertical  projection  will  be  parallel  to 
the  base  line. 

83.  Finally,  if  the  given  straight  line,  M  o,  figs..  6  and'  6°,  is 
inclined. to  both  planes,  the  projections  of  it,  mo,  m'  o',  will  hoth 
be  inclined  to  the  base  line,  A  B.  These  projections  are  in  all 
cases  obtained  by 'letting  fall,  from  each  extremity  of  the  line,  per- 
pendioulars  to  each  plane. 

The  projections  of  a  straight  line  being  given,  its  position  in 
space  is  determined  by  erecting  perpendiculars  to  the  horizontal 
plane,  from  the  extremities,  m  o,  of  the  projected  line,  and  making 
them  equal  to  the  verticals,  n  m'  and  p  u'.  The  same  result 
follows,  if  from   the   points,  m',  u',  in  the  vertical  plane,  \vc  erect 


perpendiculars,  respectively  equal  to  the  horizontal  distances 
mn  and  po.  The  free  extremities  of  these  perpendiculars  meet 
each  other  in  the  respective  extremities  of  the  line  in  space. 

THE    PROJECTIONS   Of    A   TI.ANE   SURFACE. 

84.  Since  all  plane  surfaces  are  bounded  by  straight  lines,  as 

soon  as  the  student  has  learned  how  to  obtain  the  projections  of 
these,  he  will  lie  able  to  represent  any  plane  surface  in  Hie  two 
planes  of  projection.  It  is,  in  fact,  merely  necessary  to  let  fall 
perpendiculars  to  each  of  the  planes,  from  the  extremities  of  the 
various  lines  bounding  the  surface  to  be  represented;  in  other 
words,  from  each  of  the  angles  or  points  of  junction  of  these  lines, 
by  which  means  the  corresponding  points  will  be  obtained  in  the 
planes  of  projection,  which,  being  joined,  will  complete  the  repre- 
sentations. It  is  by  such  means  that  are  obtained  the  projections 
of  the  square,  represented  in  different  positions  in  figs.  7,  7",  8,  8% 
and  9,  9".  It  will  be  remarked,  that,  in  the  two  first  instances,  the 
projection  is  in  one  or  other  of  the  planes  an  exact  counterpart  of 
the  given  square,  becau.se  it  is  parallel  to  one  or  other  of  the 
planes. 

85.  Thus,  in  fig.  7,  we  have  supposed  the  given  surface  to  be 
parallel  to  the  horizontal  plane;  consequently,  its  projection  in 
that  plane  will  be  a  figure,  m  o  /'  7,  equal  and  parallel  to  itself, 
whilst  the  vertical  projection  will  be  a  straight  line,  p'  <>',  parallel  to 
the  base  line,  a  b. 

86.  Similarly,  in  fig.  8,  the  object  being  supposed  to  be  paralle. 
to  the  vertical  plane,  its  projection  in  that  plane  will  be  the  equa, 
and  parallel  figure,  m'dp'q',  whilst  that  in  the  horizontal  plane 
will  be  the  straight  line,  m  0.     When  the  two  planes  of  pri 

are  converted  into  one.  the  respective  projections  will  assume  the 
forms  and  positions  represented  in  figs.  7",  8". 

87.  If  the  given  surface  is  not  parallel  to  either  plane,  but  yet 
perpendicular  to  one  or  the  other,  its  projection  in  the  plane  to 
which  it  is  perpendicular  will  still  be  a  straight  line,  as  j.'  ,,',  figs, 
9  and  9",  whilst  its  projection  in  the  other  plane  will  assume  the 
form,  mo  pa,  being  a  representation  of  the  object  somewhat  forjx- 
shortened  in  the  direction  of  the  inclination. 

The  cases  just  treated  of  have  been  those  of  rectangular  Bur- 
faces,  but  the  same  principles  are  equally  applicable  to  on)  poly. 
gonal  figures,  as  maybe  seen  in  figs.  1-  and  12*,  which  will  b< 
easily  understood,  the  same  letters  in  various  charm 
corresponding  points  and  perpendiculars.  Nor  does  (lie  ubtain- 
ment  of  the  projections  of  surfaces  hounded  by  curved  lines,  as 
circles,  require  the  consideration  of  oilier  principles,  as  we  shall 
proceed  to  show,  in  reference  to  tigs.  Ill  and  11. 

88.  In  the  first  of  these,  fig.  10,  the  circular  disc,  m  o  p  <;.  is  siq>- 
posed  to  bo  parallel  to  the  vertical  plane,  a  b  6  1.  and  its  projec- 
tion on  that  plane  will  be  a  eircle,  m1  o' //</',  equal  and  paralle)  to 
itself,  whilst  its  projection  on    the  horizontal  plane.  A  H  e  i>„will  he 

a  straight  line,  </  m  0,  equal  to  its  diameter.    If.  on  the  other  hand, 

thi'  disc  is  parallel  to  the  horizontal  plane,  as  in  lie.   |J,  its  vertical 

projection  will  be  the  straight   lino,  p'&m1,  whilst  its  horizontal 

projection  will  he  the  circle,  op  1,1  7. 

If  the  given  circular  disc  he  inclined  to  either  plane,  ifa 

tion   in   that  plane  will  be  an  ellipse;   and  if  it    i>  inclined    I  h 

planes,  both   projections  will   be  ellipses.      This  will   he   made  e'.  i- 


■     • 


SSL  WW  maati  tilling  Dm   projections  of  regular  figures,  it 
fariiiute*  th.  proce—  considerably  if  projections  of  the  centres  and 

<■.     -■■   .n..    -   I..-.:  f    , ■  ■>..  i.  in  i'i  ■-.  I  ■    ll.aoiM, 

\;   ft   ..  B*\  !,'..•   ;<•>•..  :i -n  ..!"».!    pUlM    SUrfacaa  may  bt   !'•  ir.  i. 
■■  u  how  in  obtain  the  ppjertions  of  points  and  line*. 
'   objects  bounded   by  surfaces 
•ad  lines,  the  f  uDitn., 


PRISMS   \\l>  OTHER  BOJJ 

I'LATK    VII. 

90.   Before  entering  1  in  the  rrpre- 

— ntitino  of  solids,  the  student  should  make  hini- 
«:-:i  -h-  imcjiy  ■  •  ..-.     .   adopted   in  aaaam  and  a". 

with  reference  to  inch  objects;  and  we  here  sabjoin  such  as  will 
b.-  n-v.-ra-y. 

t    having    thi 
that  i«.  lprucs  length,  iriMK  and  height.      a    - 

sJbs  |.^„^_,  ■afnttode,  rolmne,  or  capacity. 

There  are  ■  i 

bounded  by  plane  anrfaeea;  the  earn,  the  cylinder,  and  the  sphere, 
are  bounded  ■  KM.     Those  are  termed  solids  i/ re. 

taluJun,  which  may  be  defined  as  generat.Hl  by  the  fiulilll 
plane  a-  ;ued  the  axis.     Thus,  a  rin^', 

or  annular  torus,  U  a  -  a  circle 

angles  to  the  plane  ••  \  -..n.  the 

lateral  fa  ,,al  and 

'■ 
fiscea,  or  facets,  are  p- 
when  the  ends  are  r 
pmrmlUofiped,  when  the  ends  are  r 
and  wte  equal  and  squ. 

r  regular  kexakedrtm. 

.mlar  polyhedra,  be-  diod    by 

appropriate   names;    an  :tid    the 

inaaSedmn,  whkh   ar. 
■ 

'. 
m  a  polyhedron,  of  whkh  all   th.- 
aniiing  in  one  point,  the  o/>r.r,  and  having.  a«  bow- 

I 
and  pyramid  are  triangular,  quadrantriilar.  | 

rdinif  aa  the  p!y.'..n-   forming  the  bawi  are  b 
aa    .-.  a,  pentagons,  hi  cagona,  he 

By  the  htlgk 
eular  let  fall  ft 

!•••"■••     Iwaentl   ■;-->■       ilar  meets  the  centre  of  the  baam, 
A  tntmrmttJ  pyram  ti  of  a  pyr:. 

a  plane  para! 

may  be  demr 
g  about,  and  at  any  .  from,  a 


r.  ■  :     ik  :.r  ai  ■ 

A  eon*,  fig.  j 

termin;.  ti 
the  ba>. 

a   |nt- 

• 

ti..  baaa. 

A  sphere  is  a  solid  gener..:- 
sbout  its  dioi.  £j. 

A  spheric  u 

'■ 

■ 
obtained  will  be  annular  or 
an-,  Li.'. 

; 

A  spheric  w- 

- 
twined  .i 
A  sal  • 

.    by   tlie 

■ 

•-res. 
A  segmental  anmili.  on  of  a 

1 

. 
on  the  ai 

A  »rV  Of  pyram  itlal  I 

THE    rKOJF.  ..    A- 

91.   A  Clll-e,    of  «; 
■ 

I"  and  I. 

W 
-  parallel  to  th 

on  the 

.  ■  nlar  to   t-o'li 
straight  linos,  as  A  D  .<  I.  snd  a'  r    ai.  I 


BOOK    OF    INDUSTRIAL    DESK  IN. 


85 


hfing  respectively  in  the  same  straight  lines  perpendicular  to  the 
base  line,  l  T.  It  will  also  bo  perceived,  that  the  base,  f  e  g  h, 
fig-  <A,  cannot  be  represented  in  the  horizontal  projection,  nor  the 
side,  d  c  g  H,  in  the  vertical,  sinco  they  are  respectively  immedi- 
ately behind  and  hidden  by  the  sides,  a  b  c  d  and  aief,  repre- 
sented in  the  projections  by  the  squares,  a  b  c  d,  fig.  1*,  and 
A'  b'  e'  f',  fig.  1.  They  are,  however,  indicated  in  the  planes  to 
which  they  are  perpendicular,  by  the  straight  lines,  f'  e'  and  D  c. 

92.  "It  will  bo  evident  from  these  remarks,  that  in  order  to 
design  a  cube  so  that  a  model  may  be  constructed,  it  is  sufficient 
to  know  one  of  the  sides,  for  all  the  sides  are  equal  to  each  other. 

When  the  plans  are  intended  to  be  used  in  the  actual  construc- 
tion of  machinery  or  buildings,  the  objects  should  be  represented 
in  the  projections  as  having  their  principal  sides  parallel  or  per- 
pendicular to  the  horizontal  and  vertical  plane  respectively,  in 
order  to  avoid  the  foreshortening  occasioned  by  an  oblique  or  in- 
clined position  of  the  object  with  reference  to  these  planes,  because 
the  actual  measurements  of  the  different  parts  cannot  be  readily 
ascertained  where  there  is  such  foreshortening. 

To  obtain,  then,  the  projections  of  the  cube,  fig.  ^,  a  square 
must  be  constructed,  as  a  b  c  d,  fig.  1*,  having  its  sides  equal  to 
the  given  side  or  edge,  the  sides  a  b  and  d  c  being  disposed  parallel 
to  the  base  line  ;  next,  the  square  must  be  reproduced  as  at  a'  b'  e'  f', 
fig.  1,  on  the  prolongations  of  the  sides,  A  D  and  B  c,  which  are 
perpendicular  to  the  base  line. 

the  projections  of  a  eight  square-eased  prism,  or 
rectangular  paeallelopiped,  fig.  [b. 

93.  The  representation  of  this  solid  is  obtained  in  precisely  the 
same  manner  as  that  of  the  cube,  the  sides  being  supposed  to  be 
parallel  or  perpendicular  to  tho  respective  planes  of  projection. 
The  base  of  tho  prism  being  square,  its  horizontal  projection  is 
necessarily  also  a  square,  A  B  c  D,  fig.  2";  but  its  vertical  pro- 
jection will  be  the  rectangle,  a'  b'  e'  f',  fig.  2,  equal  to  one  of  the 
sides  of  the  prism.  For  the  construction  of  these  projections,  the 
same  datum  as  in  the  preceding  case  is  required ;  namely,  a  side  of 
the  base,  and  in  addition,  the  height  of  the  parallelopiped,  or 
prism. 

THE   PROJECTIONS   OF   A   QUADRANGULAR   PYRAMID,   FIG.    ©. 

94.  This  pyramid  is  supposed  to  be  inverted,  and  having  its 
base,  A  B  c  D,  parallel  to  the  horizontal  plane  :  it  follows  upon  this 
assumption,  that  its  horizontal  projection  is  represented  by  the 
square,  a  B  c  D,  fig.  3°.  The  axis,  or  centre  line,  o  s,  which  is 
supposed  to  be  vertical,  and  consequently  passes  through  the  centre 
of  the  base,  is  projected  on  the  horizontal  plane  as  a  point,  o,  fig. 
"",  and  on  the  vertical  plane  as  a  line,  o'  s ;  drawing  through  the 
point,  o',  of  this  line,  the  horizontal  line,  a'  b',  equal  to  a  side  of 
the  ba«e,  which  is  supposed  to  be  parallel  to  tho  vertical  plane,  we 
shaU  obtain  the  vertical  projection  of  the  base ;  and  joining  a's,  b's', 
that  of  the  whole  pyramid,  the  points  a'  and  b'  may  be  found  by 
prolonging  the  parallels,  A  d,  b  c,  fig.  3d.  This  may  be  conveniently 
done  with  the  square,  and  tho  operation  is  usually  termed  squaring 
over  a  measurement — that  is,  from  one  projection  to  another.  Tho 
lateral  facets,  sic  and  sab,  aro  represented  in  the  vertical  pro- 
jection by  the  straight  lines,  a'  s,  b'  s,  fig.  1,  since  they  are  per- 


pendicular to  the  vertical  plain';  and   the  projection  of  the  facet. 

d  s  c,  is  identical  with  a'  s  b',  that  of  the  front  facet,  a  s  ii,  imme- 
diately behind  which  it  is.    Since'  each  of  the  inclined  con 

facets  is  bidden  by  the  base,  they  cannot  he  drawn  in  sharp  lines 
in  tho  horizontal  projection  ;  wo  have,  however,  indicated  their 
positions  in  faint  lines,  fig.  3".  Were  these  lines  full,  the  projec- 
tion would  be  that  of  a  pyramid  with  the  apex  uppermost,  or  of 
a  hollow,  baseless  pyramid,  in  the  same  position  as  fig.  ©. 

THE    PROJECTIONS   OF   A   RIGHT   PRISM,   PARTIALLY   HOLLOWED, 
AS    FIG.     ©. 

95.  The  vertical  and  horizontal  projections  of  the  exterior  ..I' 
this  solid,  are  precisely  the  same  as  those  of  fig.  13;  they  are  re- 
presented respectively  by  tho  square,  a  b  c  d,  fig.  4",  and  the  rec- 
tangle, a'  b'  e'  f',  fig.  4.     It  will  be  perceived,  that  the  internal 

surfaces  of  this  figure  are  such  as  may  be  supp      J   

of  the  sides  of  a  smaller  prism  ;  the  sides,  chu  and  t  L  M  It,  are 
parallel  to  the  vertical  plane,  and  G  K  N  J  and  H  I  M  L  perpendicular 
to  it,  and  it  follows  that  the  projections  of  this  lesser  figure 
will  assume  the  forms,  g'  h'  i'  j',  fig.  4,  and  a  H  L  k,  fig.  f. 
The  lines,  K  g,  l  h,  are  faint  dotted  lines,  instead  of  being  slurp 
and  full,  as  being  hid  by  the  base,  A  B  c  D,  of  the  external  prism. 
These  lines  will  be  found  to  be  different  to  the  projection  lines,  or 
working  lines.  The  latter  are  composed  of  irregular  dots,  whilst 
those  which  indicate  parts  of  the  figure  which  actually  exist,  hut 
are  hidden  behind  more  prominent  portions,  are  composed  of  regu- 
lar dots.  This  distinction  has  been  adhered  to  throughout  tho 
entire  series  of  Plates. 

97.  On  examining  tho  examples  just  treated  of,  it  will  be  ob- 
served, from  the  horizontal  projections,  that  the  contour,  or  out- 
line, is  in  every  case  square,  whilst,  from  the  vertical  projections, 
it  will  be  seen  that  each  object  is  different  This  demonstrates 
that  one  projection  is  not  sufficient  for  the  determination  of  all  the 
dimensions  of  an  object;  and  that,  even  in  the  simplest  casi  a,  1  o 
different  projections  are  absolutely  necessary.  It  will,  moreover, 
bo  seen,  as  we  advance,  that  in  many  cases,  three,  and  at  times 
more,  projections  are  required,  as  well  as  sections  through  two  or 
more  planes. 

THE   PROJECTIONS   OF   A    RIGHT   CYLINDER,    FIG.    g. 

98.  The  axis,  o  m,  of  this  cylinder  is  supposed  to  be  vertical, 
and  its  bases,  a  b,  e  f,  will  consequently  be  horizontal.  Its  pro- 
jections in  figs.  5  and  o"  are  represented  by  tho  rectangle,  a'  d'  l>  i  ', 
on  the  one  hand,  and  the  circle,  A  c  b  d,  on  the  other.  It  is  evi- 
dent, that  to  draw  these  figures,  it  is  quite  sufficient  to  know  the 
radius,  o  a,  of  the  base,  and  the  height,  o  m;  with  I  he  given 
radius,  we  describe  the  circle,  a  c  b  d,  which  is  the  horizontal  pro- 
jection of  the  whole  cylinder;  then  making  the  vertical,  of    ■ 

to  the  given  height,  and  squaring  over  by  means  of  the  parallels, 
A  A',  b  B',  the  diameter  of  the  circle,  we  draw,  through  o'  and 
m,  the  horizontals,  a'  b',  e'  f',  completing  the  parallelogram, 
a'  b'  e'  f',  which  is  the  vertical  projection  of  the  cylinder. 

THE    PROJECTIONS   OF    A   RIGHT   CONE,   FIG.    [j?. 

99.  The  projections  of  aright  cone  differ  from  those  of  the  cyliii- 

'  der  solely  as  far  as  regards  the  vertical  plane.     Tims  it  will  he  get  n, 


' 


la  fcja.  duJC,  that  the  horiioatal  pr.;.vjon  of  the  com,  »  A  B,  ■ 

•'*-  taar  •••  that  of  a  <■;,  ',;n  !.-r  bun,-  an  e>jual   line ;  but 
liit  tcrtica.  prujertioa.  V  *'  >  -  mj»  a  nvlajr,  i*  an 

i«ii  !■■  triangle,  of  whirh  the  baa*  ia  equal  I 

isJaf  the  boruontal  projection,  whuat  Ifae  height  ia  that 

.       M        S    .1    -i 

know  I  .ircular 

Tiir.  rsojccnon  or  a  snirnr,  n<;.  ft. 

- 

■ 

radius  equal  to  that,  o  I 

- 
-    i-  a  further  illustration  of  the  in- 

we    approach    I 

»'>.-!i  aaldad  projection  would  equally  represent   that  of  a  cylinder 

with  a  h.  mi -;■!;•  -ii-;i!    termination,     'i 

•h.   riantad  proj  etions  of  cylinder  and  >■■•  :10a,  mod,  indeed,  to  a!l 

aaldbodata. 

•  which 

repreae:  I 

■ 

'i  of  lines  are 

•  maintenane. 

•it  and 
particular  dire.  I 

tliat  some  par- 
•*hil»t  others  ai  Hitherto,  a  nniform 

that  it  -  il.  a  0,  of  ill" 

■ 

V. 
■r,  and  on  wliat  account  it  H 


ia  the   r.  ,.n— 

i  roJ,  ia  our  drs  • 

.  k  and  a',  in  ;  aa  the 

and  uu;> 

tical  or  horizontal  plane,  the  turning  avii  ! 
the  baae  tine.     Let  us  in  the.  lir.-t  (dace.    - 

|>lanc  at  o,  and  in  Ili<>  vertical  at  a'. 
and  rail 

f..ldi*l  ■: 

- 

elination  ion  ihu 

■ 
1 
part  ol 

- 

. 

the  lines,  B  1 . 
'  : .'.     It  moat  b 
■ 
projection,  ia   1 

_r   in  a  similar   manner.     What    ha*  jnat 
- 

parti  which  . 

tit  and    in    the    ahadi 
rhich  are  illuminated,  from  '.,  not. 

■  '■ 

I 
not  be  employed  as  that  fori 
minent  surface.    Thm  "    the  line*,  b'    ' 

N 

those  on    the    ilhllllillM.il    ride  of    - 
- 

i*  in   the  shade.      In  other  * 

fully  illuminati'd    outline,   a  t  da,   an. I 

that    portion  .    in    the 

aavily  l«.  full  • 
anea  entirely  ; 


BOOK  OF  INDUSTRIAL  DESIGN. 


In  the  horizontal  projection  of  the  cylinder,  fig.  5°,  the  illumi- 
nated portion  corresponds  to  the  semi-circle,  o  rf  4,  whilst  that  in 
the  shade  is  the  other  semi-circle,  a  c  b;  the  points,  a,  b,  of 
separation  of  the  two  halves,  are  obtained  by  drawing  through 
the  centre,  o,  a  diameter,  a  b,  perpendicular  to  the  ray  of  light, 
d  o,  or  by  drawing  a  couple  of  tangents  to  the  circle  parallel 
to  this  ray.  The  straight  line,  a  b,  is  inclined  to  the  base  line 
at  an  angle  of  45°.  Great  care  is  necessary  in  producing  the 
circular  shadow-line,  acb,  and  the  nibs  of  the  drawing-pen  should 
be  gradually  brought  closer  as  the  extremities,  a  and  b,  of  the 
shadow-line  are  approached,  so  that  it  may  gradually  die  away 
into  the  thickness  of  the  illuminated  line.  By  inclining  the 
drawing-pen,  or  by  pressing  it  sideways  against  the  paper,  the 
desired  effect  may  be  produced;  the_  exact  method,  however,  being 
obtained  rather  by  practice  than  by  following  any  particular  in- 
structions. A  very  good  effect  may  also,  in  some  instances,  be 
produced,  by  first  drawing  the  entire  circle  with  the  fine  line,  and 
then  retracing  the  part  to  be  shadow-lined  with  a  centre  slightly 
to  one  side  of  the  first  centre,  and  repeating  this  until  the  desirefl 
strength  of  the  shadow-line  is  obtained. 

104.  In  the  plan  of  a  cone,  fig.  6°,  the  part  in  the  shade  is  always 
less  than  the  part  illuminated ;  but  it  requires  an  especial  con- 
struction, which  will  be  found  in  the  chapter  treating  of  Shadows, 
for  the  determination  of  the  lines  of  separation,  se;  and  it  is  sel- 
dom that  smh  extreme  nicety  is  observed  in  outline  drawings,  the 
shadow-line  of  the  plan  of  the  cone  being  generally  made  the 
same  as  that  of  a'  cylinder,  or  perhaps  a  little  less,  according  to 
the  judgment  of  the  artist.  Yet,  if  the  height  of  the  cone  be 
less  than  the  radius  of  the  base,  the  whole  conical  surface  will  be 
Llumina:cd,  and  consequently  its  outline  should  have  no  shadow- 
iine. 

105.  In  explanation  of  the  motives  which  have  guided  us  in 
the  adoption  of  the  diagonal  of  a  cube,  as  projected  in  the  lines, 
R,  r',  fig.  8,  as  the  direction  of  the  rays  of  light,  in  preference  to 
the  other  systems  proposed,  we  shall  proceed  to  point  out  some 
of  the  inconveniences  attending  the  latter. 

In  the  first  place  it  must  be  observed,  that  if  we  adopt,  as  the 
direction  of  the  rays  of  light,  the  diagonals  projected  in  a'  e'  and 
D  B.  figs.  1  and  1",  that  part  of  the  object  which  is  represented  in 
the  plan  as  illuminated,  does  not  correspond  with  the  part  repre- 
sented as  illuminated  in  the  elevation  :  in  such  case,  the  shadow- 
lines  would  be  A  B  and  B  c  in  the  horizontal  projection,  and  f'  e', 
d'  e'  in  the  vertical,  so  that  ihere  is  no  distinction  made  between 
the  plan  and  the  elevation;  whereas,  according  to  the"  system 
adopted  by  us,  it  is  at  first  sight  apparent  which  is  the  plan,  and 
which  the  elevation,  from  the  mere  shadow-lines,  which  are  in  the 
latter  at  the  lower  parts  of  the  object ;  whilst,  in  the  former,  they 
are,  on  the  contrary,  at  the  upper  parts.  It  is  not  natural,  more- 
over, to  suppose,  that  in  the  representation  of  any  object,  the  light 
can  be  made  to  come  as  it  were  from  behind  the  object,  for  in  that 
case  the  side  nearest  the  spectator  would  evidently  be  in  the 
shade  ;  and  yet  it  is  only  on  such  a  supposition  that  the  projections 
of  the  ray  of  light  can  be  such  as  D  b  and  a'  e'.  Thus  a  double 
inconvenience  may  be  urged  against  this  system. 

If,  on  the  other  hand,  the  rays  of  light  are  supposed  to  be  per- 
pendicular to  either  plane,  such  confusion  will  result  as  to  render 


it  impossible  to  ascertain,  by  any  reference  to  1 1  r< •  shadow-linos 
what  is,  or  what  is  not,  illuminated,  and  thus  the  object  of  employ- 
ing shadow-lines  would  be  lost  sight  of.      Thus  let  US  suppose,  for 

example,  that  the  light  is  perpendicular  to  the  vertical  plane, 
whence  it  follows  that  the  whole  of  the  anterior  facet,  tigs.  1  to  1, 
is  fully  illuminated ;  but,  at  the  same  time,  all  the  facets  perpen- 
dicular to  the  vertical  plane  are  equally  in  the  shade,  and  it  would 
consequently  bo  necessary  to  use  shadow-lines  all  round,  or  el  e  not 
at  all;  and  whichever  plan  was  adopted,  would  lie  quite  unintelligi- 
ble. Besides  this,  it  is  unnatural  to  suppose  that  the  spectator 
should  place  himself  between  the  light  and  the  object.  Indeed,  it 
is  unquestionable  that  the  most  appropriate  direction  to  he  given  to 
the  ray  of  light,  is  as  before  stated,  that  of  the  diagonal  of  a  cube, 
of  which  the  facets  are  respectively  parallel  to  the  two  plane,  of 
projection;  and  tho  projections  of  this  diagonal  are,  consequently, 
inclined  to  (he  base  line  at  an  angle  of  45°,  hut  proceeding  from 
above  in  the  vertical  projection,  and  from  below  in  the  horizontal 
projection,  as  shown  by  the  arrows,  R  and  r',  fig.  8. 

PROJECTIONS  OF  GROOVED  OR  FLUTED  CYLINDERS 
AND  RATCHET  WHEELS. 

PLATE  YIII. 
106.  The  various  diagrams  in  this  plate  are  designed  principally 
with  the  view  of  making  the  student  practically  conversant  with 
the  construction  of  the  projections  of  objects:  an  I.  besides  teach- 
ing him  how  to  delineate  their  external  contours,  to  enable  him  to 
represent  them  in  section,  that  their  iutei  ire  maj  also  lie 

recorded  on  tho»drawing. 

Fi|fs.  1  and  1°  are,  respectively,  the   plan    and   elevation  of  a 
right  cylinder,  which  is  grooved  on  its  entire  external  surface.     The 
grooves   on    one-half   of  the  circumference    are   supposed    to    I" 
pointed,  being  formed  by  isosceles  triangles  of  regular  dinioii 
sions,  and  may  represent  the  rollers  used  in  Sax  machinery,  i:i 
apparatus   for   preparing   food   for  animals,  and   in    inanj 
machines.     Tho  other  half  of  the  circumference  is  ton  u 
square  or  rectangular  grooves,  the  lateral  faces  of  which  are  I  ithi  t 
parallel  to  the  centre  lines  which  radiate  from  tin    i 
themselves  radiating. 

107.  To  construct  the  horizontal  projection  of  this  e; 
that  is,  as  seen  from  above,  we  must  first  ascertain  bow  many 
grooves  are  contained  in  the  whole  circumference  ;  then  drai 
circle  with  a  radius,  A  o,  which  should  always  be  greater  than  that 
of  the  given  cylinder,  divide  it  into  twice  as  many  equal  parte  as 
there  are  grooves.  If  the  student  will  refer  back  to  the  section 
treating  of  linear  drawing,  illustrated  in  Plate  I.,  he  will  find  simple 
methods  of  dividing  circles  into  2,  3,  4,  6,  8,  and  12  equal  ports, 
and,  further,  of  subdividing  these.  Thus,  as  the  cylinder, fig.  l, 
contains  24  grooves,  its  circumference  must  be  divided  into  48  equal 
parts.    To  obtain  these,  begin  by  drawing  two  diameters,  a  b,  c  n, 

perpendicular  to  each  other;  then,  from  each  extremity,  mark  oil'  the 

length  of  the  radius,  to,  thus  obtaining  the  four  points  numbered 

8  on  one  side,  and  the  points  numbered  4  on  the  other — making, 
With  the  points  Of  intersection  Of  the  two  diameters  with  the  cir- 
cumference, in  all,  12  points.  It  remains  simply  to  bisect  each 
space,  as  a 1,  b — 4,  or  4 — 8,  &e.,  as  well  as  the  lesser  spaces 


' 


thus  toand;  thu  will  r>e  the  48  divisions  required.      I 
the  potato  of  dm*..o  draw  li,  which  will  ditide 

the  inner  cirri*  iWrilii  il    with  the  radiu-  ■•  tame 

noiaUr  of  equal   part*.     The  depth   of  the  grooves  is  limited 
..-vriDHl  with   Uir  radius,  o  E,  whilst   the  outside 
omening  ridge*  is  defined  bg 
All  the  opera!. 

i:    Mm    .-  :-••!>.'     :.  .  :     ■    ■■.•'.■    '  ..-.,  irah4  hvlan.'ulal  .t.-uv 
Id  pro  ceding,  we  mu«t.  in  the  former  case. 

ti.  a.  I.  r.  d.  «lih  h  are  in  earn  circumference  alternately; 

it  have  simply 
%  as  well  as  the  radial 

•■••■• 
the  depth  ahould  be  given,  aay  m  i 
two  horizontals,  M  f.  ■ 

to  •  •!•. 

iiid   draw   parallels    : 

rior  of  Out  [tirt  of  the 
/ontal,  M  r. 

m  not 
■■ 

1  and  P.  that 
tin-  interior  of  the  cylinder. 
ivntral  citvu!.  -  Dot  ap- 

parent 

1  1'.  It  i-.  im- 
of  the 

through 

to  the  pi 

■ 

- 
tin-  in- 

in  an  •  •'■• 

.  t  from 

Th»t  » hich 

•n*l   piano  passe*,  i- 

,'irtn  which  the  plane 
\v  the 
parts  in 

iron,  a 

•  :..■»•'   -t.  .  :•      .   .i~    I.  W'liiUt  .1   lighter  "tie  ilnlicati  «   wood  or  .ti.tie  ; 

r.  indicates 


the  object  to  be  made  of  copper,  whilst  tiui  b  fig.  J*  correspond* 
to  cast-iron,  and  in  fig.  3*  to  wood  or  masonry. 

that  the  actio*  Una,  of  whatever 
deacriptiiin  they  may  be,  are  always  inclined  at  an  angle  of  45* 
with  the  baae  line ;  this  is  to  distinguish  the  anrttonmg  from  fiat 

- 
less  prominent  than  another:   this  latter  flat-tinting  it  generally 

■  ;■  ndirular  or  horizontal  lines.     Tike 

mdiralwa  the  base  of  the  internal  cylinder,  cat,  ahould  not  be 
a  shadow-tine  equal  in  strength  to  tie  bases  of  the  sectional  parts, 
for  the  latter  are  more  prominent.  This  point  is  seldom  attended 
to  as  it    slum  Id    be;  greater  beanty   and   •' 

This  remark  applies  equally  to  all  projertiona 

•'  portion  is  more  prominent  than  another. 

Thus,  ;-  .'.  the  vertical  lines  passing  through  r   are 

considerably  in  I  than  those  passing  through  H  w , 

and  lying  in  a  poaawinr  flan*.      It  is  the  more  important  to 

u  in  rapraw  •  ' 
least  as  much  as  poe>j 

■  ■.n-jderatioD   •  1  and  3, 
representing  ratchet  wbeab  ami   fl 

intelligi  rationa  a*  an-  a 

d  quite  obvious  by  the  view!  th«m~ 


THE  ELEMENTS  OF  ARCHITECTURE. 

H.ATK    IX. 
111.  Columns  of  tl 
quently  employed  in  buildings,  and  also  in  mcvliani. .. 

i 
I.  Ti,.  Taw 
D 

3.  Th 

4.  Tie      ' 

5.  Ti. 

I 
11.'    I 

■ 

ami  the 

- 

nine    time*:    the    Corinthian    and    I  The 

■ 
ent  pari  - 

•     he  lower  pari 

■ 

ir»   ».!h»r»J   to  is*  fin.  h*w  i»,nf  of  n  . 

a  sstWnir  .  bvt  »•  on  i4  folis,  is  th  • 
i  r«  on.r»   rru.it.  a  asjat  is 

IS*  Ant  .    ■*  j.r..  ,.g 
r.rk,    Ron.,,.    uJ    M  •!.  r» 
loauc  .   sail  Um  laird.  C-i.>il.u  uut  (  uaiaal*. 


BOOK  OF  INDUSTRIAL  DESIGN. 


into  i2  parts,  in  the  Tuscan  and  Doric  orders;  and  into  18  parts, 
in  the  Ionic,  Corinthian,  and  Composite.  The  whole  height  of 
the  Tuscan  order  is  22  modules  2  parts,  apportioned  as  follows : — 
The  column  is  14  modules;  the  pedestal,  4  modules  8  parts ;  and 
the  entablature,  3  modules  6  parts.  The  whole  height  of  the 
Doric  order  is  25  modules  4  parts — the  column  being  16  modules; 
the  pedestal,  5  modules  4  parts ;  and  the  entablature,  4  modules. 
The  whole  height  of  the  Ionic  order  is  28  modules  9  parts — the 
pedestal,  6  modules;  the  column,  18  modules;  and  the  entablature, 
4  modules  9  parts.  The  wfiole  height  of  the  Corinthian  and 
Composite  orders  is  31  modules  12  parts — of  which  6  modules  12 
parts  form  the  pedestal,  20  modules  the  column,  and  5  modules 
the  entablature. 

As  we  do  not  propose  to  treat  especially  of  architecture,  we 
have  not  given  drawings  of  all  the  various  orders,  but  have  con- 
fined ourselves  to  the  Tuscan,  as  being  the  simplest,  as  well  as  the 
one  more  generally  adopted  in  the  construction  of  machinery. 
At  the  end  of  this  Chapter,  will  be  found  tables  of  the  dimensions 
of  the  various  components  of  the  Tuscan  order,  and  we  also  there 
give  a  similar  tab:3  for  the  Doric  order. 

OUTLINE   OF   THE   TUSCAN   ORDEK. 

113.  The  whole  height  being  given,  as  M  n,  the  proportions  of 
the  different  parts  may  always  be  determined.  Let  tins  height 
be,  for  example,  4  metres  272  millimetres,  fig.  7.  First,  divide  it 
into  19  equal  parts,  then  take  4  such  parts  for  the  height  of  the 
pedestal,  12  for  that  of  the  column,  and  the  remaining  3  for  the 
entablature.  Then,  according  to  the  order  which  it  is  intended  to 
follow,  the  height,  m  n,  of  the  column,  is  divided  into  7,  8,  9,  or  10 
equal  parts,  and  the  diameter  of  the  lower  part  of  the  column  will 
be  equal  to  one  of  these  divisions :  thus,  in  the  Tuscan  order,  the 
diameter,  a  ft,  is  \  of  the  height,  m  n ;  the  half  of  this  diameter, 
or  the  radius  of  the  shaft,  is  the  unit  of  proportional  measurement, 
called  the  module,  and  with  which  all  the  components  of  the  order 
are  measured :  it  follows  then,  that  in  the  Tuscan  order  this  mo- 
dule is  T'T  of  the  height  of  the  column,  in  the  Doric  ~j,  in  the 
Ionic  T's,  and  —^  in  the  Corinthian  and  Composite. 

114.  The  three  members  of  an  order  are  each  subdivided  into 
three  divisions.  Thus  the  Pedestal  is  composed  of  the  Socle, 
or  lower  Plinth,  a  ;  of  the  Dado,  B  ;  and  Cornice,  c  :  the  column 
consists  of  the  Base,  or  Plinth,  D  ;  the  Shaft,  E  ;  and  the  Capital,  f  ; 
and  in  the  entablature  are  the  Architrave,  G ;  the  Frieze,  H ;  and 
the  Cornice,  L 

115.  Before  proceeding  to  delineate  these  different  parts,  and 
the  mouldings  with  which  they  are  ornamented,  it  is  expedient  to 
set  off  a  scale  of  modules,  determined  in  the  manner  just  stated, 
the  module  being,  of  course,  subdivided  into  12  equal  parts. 

To  make  the  mouldings  and  various  details  more  intelligible, 
we  have  drawn  the  various  portions  of  the  order,  separately,  to  a 
larger  scale.  Thus  the  socle  and  pedestal  of  the  column  are  repre-. 
sented  in  elevation  in  fig.  2,  and  in  plan  in  fig.  3,  to  a  scale  2 \  times 
that  of  the  complete  view,  fig.  1,  and  the  module  will,  of  course,  be 
proportionately  larger.  All  the  numbers  indicated  on  these  figures, 
give  the  exact  measurements  of  each  part  and  each  moulding,  so 
that  they  may  be  drawn  in  perfect  accordance  with  the  scale  given. 
It  conduces  considerably  to  the  symmetry  and  exactitude  of  the 


drawing,  to  set  off  all  the  measurements  from  the  axis  or. Centre 
line,  c  ■/.  The  module  being  but  an  arbitrary  measurement,  ii  is 
necessary,  in  practically  carrying  out  any  design,  to  ascertain  the 

different  measures  in  metres  and  parts  of  metres ;  and  for  this 
reason  we  have  given  additional  scales  in  metres,  to  correspond  to 
those  in  modules ;  and  we  have  also  expressed  in  millimetres,  on 
each  figure,  tho  measurements  of  the  various  details,  placing  the 
metrical  in  juxtaposition  with  the  modular  ones.  And,  to  give  a 
distinct  idea  as  to  the  degrees  of  prominence  or  relief  of  the 
various  members,  a  part  of  tho  elevation  is  shown  as  sectioned 
by  a  plane  passing  through  the  axis  of  the  shaft,  this  part  being 
sufficiently  distinguishable  from  the  sectional  fiat-tinting.  In 
the  horizontal  projection,  fig.  3,  are  also  represented  portions  of 
sections  in  two  different  planes,  one  being  at  tho  height  of  I  he 
line,  5 — 6,  and  the  other  at  that  of  7 — 8.  The  first  shows  that  the 
shaft  is  round,  as  well  as  the  fillet,/,  and  the  torus,  g,  whilst  the 
base,  h,  and  cornice,  ij,  are  square:  tho  second  section  shows, 
in  a  similar  manner,  that  the  dado,  b,  the  socle,  a,  and  its  fillet,  /), 
are  square.  The  tlat-tintings  sufficiently  indicate  the  parts  in 
section. 

Fig.  4  represents  the  entablature  and  the  capital  of  the  column 
in  elevation  and  in  section.  Fig.  5  is  a  horizontal  section  of  the 
column  with  its  capital,  as  it  were  inverted,  and  is  supposed  to  be 
half  through  the  line,  1 — 2,  and  half  through  3 — I.  The  whole 
is  what  is  termed  a  false  section,  the  parts  in  section  bring  in 
parallel,  but  not  identical  planes.  The  different  measurements 
are  given  in  modules  and  metres,  as  in  the  other  figures;  they 
indicate  tho  respective  distances  from  the  axis.  <■'  </'. 

116.  The  execution  of  this  design  offers  little  or  no  difficulty] 
but  all  the  operations  required,  as  well  as  the  parts  to  which  the 
measurements  apply,  are  carefully  indicated.  It  is,  therefore, 
unnecessary  to  enter  into  further  details,  except  as  far  as  relates 
to  such  parts  as  involve  some  peculiarity  :  the  shaft  of  the  column, 
for  example,  and  one  or  two  of  the  mouldings. 

Referring,  in  the  first  place,  to  the  column,  it  is  to  be  observed 
that  it  is  customary  to  make  the  shaft  cylindrical  for  one  third  of 
the  height,  that  is,  of  equal  diameter  throughout  that,  extent  : 
above  that  point,  however,  it  diminishes  gradually  in  diameter  up 
to  the  capital.  This  taper  is  not  regular  throughout,  being 
scarcely  perceptible  at  the  lower  part,  and  becoming  more  and 
more  convergent  towards  the  top.  Its  contour  is  consequently  a 
curve,  instead  of  a  straight  lino.  This  curvature  constitutes  what 
is  termed  the  entasis,  and  is  employed  to  correct  the  appaient 
narrowness  of  a  rectilinear  column  at  the  middle.  Such  defective 
appearance  onl*takes  place  "hen  the  cylindrical  piece,  or  column, 
is  between  a  pedestal  and  an  entablature  having  plane  surfaces 
A  cylinder,  or  sphere,  always  seems  to  occupy  less  space  than  a 
plane  surface  equal  to  its  greatest  section.      Thus  the  outline  of  a 

cylinder  or  sphere,  appears  to  grow  less  when  it  is  shaded.  \..\\, 
where  the  column  is  in  contact  with  the  plane  surface  of  the  pe- 
destal or  entablature,  it  cannot  appear  less  in  proportion,  the 
proximity  of   the    latter    correcting    such    appearance,    whilst    tho 

influence  is  less  felt  at  the  central  part,  which  is  farthest  from  the 
pedestal  and  entablature.  A  true  cylinder,  therefore,  in  sach 
position,  appears  to  be  thinner  at  the  middle,  and  this  is  corrected 
bf  the  entasis,  or  curved  contour. 


«nJ   it 

eolunuu  for  m. 

and  ihr  ci.luii  ■. 

meduvtiad  entasis,  \-  ■ 

- 
»nd   increaiwxl  width   in   tin-   middle 
•uch  r»\  U 

height 

oft,  int. i  any  SI  :ti  Iht 

■ 
uucof  i  rir  ,ual   to  9}  nar-- 

.-.  C  </",  tiii.n  [Kindle!   Kali 
•.  j-  :  divide  t)n-  are,  r  j,  into  *i\  equal  porta, 
and  then  thfOWgh  the  | 

■    tin-  horicontal 
«n  throu^  li. 

od  through  d  the  ra- 

the ahaft    Thi  - 

•  J,  will 
shaft 
In   tfa  '    will    1«.  found   t«" 

.  •     .  .  i  of  the  cijmn 

lii  peculiaritiee 
1  Bopm  the  • 
!  /-  and  accompanying  minor  mould- 

■ 
teparately,  and  on  a  larger  scale,  in  figs.  9  H 


ftl  I  i:s  and  PRACTICAL  DATA. 

Tlli 

117.  V.  that  the  Yolumeoreolidity  of  abody, 

■pace  enthral  —length, 


width,  i  I  .1.  ptli, 

of  a  »oud    ia  d 

a  unit  ■•  it  u  I  square 

timetre,  and    tin*    eul. 

■ 

\\1iil-.t    i  mi 

I    i  iMla    (10*  x   10*   x    10*-=)    100 

..■•  x  loir  = 
=  (  Iikhj  -/.  x  1000  */.  x  1000"/.  =  )    i  '.    euhfa 

inillimr' 

■  1    <T     ,  ,      ',  , 

B 

. 
and  in  for — 

1  euhk  foot  —  1  yard  x  1  yard  >.  | 

and  an  I: 

119.   Para  >. — The  volumi 

• 
:  PL  7.    Let  A] 

and  K  II        11   bet      Than    the   lm.-w  =  14  X  14  a  1 
.' 
! 
■sod  by  the  I 

•    which   one  aide  UK 

.    -  1   I    •    1   l    ■;   1  1.  or  II':  j  T  . 
■  ral,  tin-  \  •  •! mm-  of  a  ri^'lil  prism,  v. 

equal  t..  tin-  product  of  tlir  baae  into  il»'  height 


TABLE   OF   SURFACES,    A5D    VOLUMES   OF    REOl  I   IB    !  -  •:  '.  III.HU  4. 


Ntniu  or  Sidi.. 
4   .   .   .  . 

19  ...  . 


N»irs  Svirici.  Vomi 

adron l-TM    >oa "11 

ii      v  dron,  or  Cube I  

Iron B'4641016 -ft 

♦ 1  I  ■ 

•M  .  .  .  .        I               oi ' B-660U&40 - 


120.  Pyram  jonal  pyramid   ■ 

to  it»  ba». 

'  I  Band  AD 

■f  the  pyramid 
1-4x1 


Ml.ll.-1. 


Tow  •■ 

|iri«in.  hating  »• 


equal  t..  the  product  of  a  third  of  the  height,  int.>  Iht  ana 
tw..  l.i-.  ■  added  to  li  of  their  product 

»    Time.       \  onl  the  volume  of  a  truneated  pyramid,  of 

which  tli.  hi      ■.  II.      8  R  • '.  ill"  lowi  r  I 
i  .  we  hart — 

V=^  x   (11+  !!'+♦  UTT')  = 


—  x  (8  a  f.  +  4  a.  f.  +  4/0  x  4)  =  I 


BOOK  OF  INDUSTRIAL  DESIGN. 


In  practice,  when  there  is  little  difference  between  the  areas  of 
the  bases,  a  close  approximation  to  the  volume  is  obtained  by- 
taking  the  half  of  the  sum  of  tho  bases,  multiplied  into  the 
height.     Thus,  with  the  preceding  data,  we  have 

/B  +  B'\ 
V  =  II  X  ^— \ — J  =  15  sq.  ft. 

121.  Cylinders. — The  cubic  contents  of  any  cylinder,  as  fig.  g, 
is  equal  to  the  product  of  the  base  into  the  height.  Thus,  in  the 
case  of  a  cylinder  of  a  circular  base,  we  have  B  =  n  R2  (72)  ;* 
consequently,  the  volume,  V,  =  jt  R2  X  H. 

First  Example. — What  is  the  volume  of  a  cast-iron  cylinder, 
of  which  the  radius,  R,  =  20  inches,  and  the  length,  H,-  =  108 
inches? 

V—  3-1416  X  20s  X  108  =  135,717  cubic  inches. 
The  volume  may  also  be  derived  from  the  diameter  of  the  cylin- 
der, in  which  case  we  have — 

:Da 


V  = 


X  II;  or, 


V  =  -7854  x  40-  X  108  =  135,717  cubic  in. 
The  convex  surface  of  a  right  cylinder,  when  developed,  is  equal 
to  the  area  of  a  rectangle,  having  for  base  the  rectilinear  develop- 
ment of  the  circumference,  and  for  height  that  of  the-  cylinder. 
It  is  therefore  obtained  by  multiplying  the  circumference  into 
the  height  or  length.  With  the  data  of  the  preceding  case,  the 
convex  surface  is  expressed  by  the  formula — 

S  =  -2n  R  X  H,  or  n  D  X  II  =  31416  X  40  X  108  = 
13,571-7  cubic  inches. 
The  volume  of  a  hollow  cylinder  is  equal  to  the  difference  between 
that  of  a  solid  cylinder  of  the  same  external  radius,  and  that  of 
one  whose  radius  is  equal  to  the  internal  radius  of  the  hollow 
cylinder.  Or,  it  is  equal  to  the  product  of  the  sectional  area  into 
the  height,  such  area  being  equal  to  the  difference  between  two 
circles  of  the  external  and  internal  radius,  respectively. 

Example. — It  is  required  to  find  the  volume,  V,  and  the  internal 
surface,  S',  of  a  steam-engine  cylinder,  including  its  top  and  bottom 
flanges  in  the  volume.  Let  the  following  be  the  dimensions : — 
External  diameter,  D,  =  56  inches ;  internal  diameter,  D',  =:  50 
inches;  length  or  height,  H,  =  120  inches;  external  projection 
of  the  flanges,  F,  =  5  inches,  and  their  thickness,  E,  =  4  inches. 
Then,  for  the  internal  surface,  we  have — 

S'  =  3-1416  x  50  x   120  =  18,850  sq.  in. 

For  the  volume  of  the  body  of  the  cylinder,  we  have — ■ 

«562      7to0- 
V'  =  — t j-    x  120=  (-7854  x  56=)— (-7854  x  502)  x 

120  =  60,000  cubic  inches. 
And  for  the  additional  volume  of  the  flanges — 

y.  =  n  (56  +  10)=  _  1562  x  4  x  2  =  (.7854  x  66=)  - 
4  4 

(-7854  x  562)  x  8  =  7666  cubic  inches. 
Whence  the  whole  volume — 

V  +  V*  =  67,666  cubic  inches. 


•  When  we  wish  to  refer  the  student  to  any  role  or  principle  already  giv> 
w#  do  so  by  means  of  the  number  of  the  paragraph  containing  such  rule  or  priri 
pie.     In  Ihr  present  instance,  what  is  refeired  to  will  be   found  at  page  20. 


122.  Corns. — The  cubic  content  of  a  cone  is  equal  to  the  pro- 
duct of  its  base  into  a  third  of  its  height ;  or, 

V  =  B  x  *L 
3 

In  the  right  cone,  fig.  \?,  of  which  the  base  is  circular — 

V^R^xH-^x^ 
3  ~     4  3 

and  as  n,  or  3-1416  -=-  (4  x  3)   =  -2618,  the  formula  resolves 
itself  into — 

V  =  -2618  x  D2  x  H. 

Example. — What  is  the  volume  of  a  right  cone,  of  which  the 
height,  H,  =  24  inches,  and  the  diameter  of  the  base,  or  D,  = 
17  inches? 

We  have — 

V=-2618  x  172  x  24  =  1816  cubic  inches. 

As  wo    shall    demonstrate,  at    a  more    advanced   stage,   the 

development  of  the  convex  surface  of  a  right  cone  is  equal  to  tno 

sector  of  a  circle,  of  which  tho  radius  is  the  generatrix,  and  the 

arc  the  circumference  of  the  base  of  the  cone — consequently,  tho 

conical  surface  is  equal  to  the  product  of  the  circumference  of 

the  base  into  the  half  of  tho  generatrix:  whence  is  derived  the 

following  formula. : — 

G 
S  =  In  R  x  ■7j-=x  R  x  G. 

Willi  the  data  of  the  foregoing  example,  and  allowing  (ho 
generatrix  to  be  equal  to  25|  indies,  we  have — 

S  =  3-1416  x  8-5  x  25-5  =  681  cubic  inches. 

123.  Frustum  of  a  cone. — The  volume  of  the  frustum  of  a  cone 
may  be  obtained  in  the  same  manner  a»  that  of  the  truncated 
pyramid  (120).  The  convex  surface  of  a  truncated  cone  is  equal 
to  the  product  of  half  the  generatrix  of  the  frustum  into  the  sum 
of  the  circumferences  of  the  bases,  and  is  expressed  in  the  follow- 
ing formula : 

S  =^  x  In  (R  +  R')  =  L  x  *  (R  +  R'). 

Example. — Let  the  length,  L,  of  the  generatrix  of  the  couie 
frustum,  =  14  inches;  the  radius,  R,  of  the  lower  base,  =  8-5 
inches;  the  radius,  R',  of  the  upper  base,  =  3-8  inches;  then  tho 
convex  surface— 

S  =  14  x  3-1416,  x  (8-5  +  3-8)  =  54  square  inches. 

124.  Splure. — The  volume  of  a  sphere  may  1  e  ascertained  as 
soon  as  its  radius  is  known.  Its  surface  is  equal  t"  foul  times 
that  of  a  circle  of  equal  diameter.  This  is  expressed  by  the 
formula — 

S  =  in  R2  =  n  D2  =  31416  x  D-, 
or  the  square  of  the  diameter  multiplied  by  3-1416. 

The  volume  is  equal  to  the  product  of  the  surface  into  one-third 
of  the  radius,  as  in  the  formula — 


V  =  1*  R2 


R 


=—  x  rt  RJ,  or  V  : 
3        3 


4188  x  R»: 


or,  if  we  employ  the  diametral  ratio — 
D 


D2  x 


—  —  -5236  x  D3 
6 


-. 


TMK    l'K\<TI«\I.    I>K.V 


VsTm;ir.—\\'e  w.u!J  kaow  whs!  i.  the  surface  and  the  volume 
V  a  •]**•«»,  of  which  the  ifianutsr  ■■■■■ll  SS  inches. 

The  mutt*  4 

•      1416=  1963-5  sq.  inchea 
IWiiIibi 

cubic  inch**. 
.  1  the  nJitt*  or  diameter  of  a  sphere,  of  which  the  volume 
:ivert  the  preceding  operation*,  the 

V  V 

R'  = 


R  = 


D'  = 


D  = 


which,  with  the  preceding  data,  gives  R  =  125  inches,  and  D  = 

•_:,    |  :..  v 

The  raiios  is  derived  Mm  the  surface  by  means  of  the  follow. 
ing  formula : — 

U«' 


R'  = 


» ).-  m. 


vhr  aes, 


R  "  \ 


D'  = 


V  31416' 


N/Arric  actors,  ferments,  and  zones. — The    surface  of  a* 
fooe  or  spheric  segment,  is  equal  t  -  ,  rvurn- 

fereoee  the  sphere,  i:  f  the  zone  or 

■ 

S  =  V  B  X  H. 
- 

'udiu*,  R,  of  the  sjihfrc,  75  inches,  the  surface— 

.   -      . 

•  >r  is  equal  to  the  pr. duct  "f 
-ical  base,  into  one-third  the  radius  of  the  sphere 
of  which  it  »  a  [• 

I  re— 

R       3 

-«xB*B       .     ■;   ■    IT       II 

'  .me  of  the  spheric  sector,  whose  spheric 

baa*  is  equal  to  the  surface  considered  in  the  previous  example,  is— 
V  =  3094  x  7  5'  X  15  =  17668  cubic  inches. 
The   volume   of  s  sfharfa  •epment  is  equal  to  the  pr 

:>c-aixth 

...    II 


Esamjir.—X.  Sea,  and  II    15  inrhrs;   the  then 


aBO 


V  =  -5»96  x  6-5'  x   1  5  =  S3  56  cubic  inches. 

The  volume  of  a  spheric  aagwk  is  equal  to  the  orodocl  of  lh* 
gore,  which  is  Ha  base,  into  a  third  of  the  radius. 
The  formula  b — 

V  ■ 

3 

where  A  =  the  area  of  the  get*. 

The  volume  of  a  zonk  segment  ia  equal  to  half  the  sum  of 
Ha  basea*  multiplied  by  ita  height,  paws  the  volume  of  a  sphere 
of  which  that  height  is  the  diameter ;  whence  the  formula — 

v-(-»!±*^)xi     " 

Ooas-vstKsss. — The  volumes  of  spheres  are  proportional 
to  the  cubes  of  their  radfi,  or  diameters.     Law  V   s 
culiic   inches,   and   r  =  4-188   cubic   inches.     It   will   he   found 
that  the  respective  radn  are— 

r  ~  v  <188  ~  V  * ls8  ~   : 

and,  consequently.  D  =  3  and  J  —  ± 

The  cubes  of  these  numbers,  that  is,  37  and  8,  have  the  same 
ratio  to  each  other  as  the  volumes  given ;  that  is  to  say — 

137  :  V188. 

When  of  equ  .  l.-rs  are   to  each   other,  as  well  as 

as  the.  squares  of  the  radii  of  their  bases. 

of  equal   diameter,  these  solids  are  to  each  other  as 

First,  then,  we  ha 

V  =  «  R»  x  H,  andr  =  «  r»  >    H. 

whence, 

V  :  t  ::  R:  :  r> 

And,  aecon  I 

V  =  «R'  x  II,  andr  =  *  R>  x  a; 

vw  *»■  • . 

V  :  i  ::  H  :  K 

TV  volume  of  a  sphere  is  to  that  of  the  circumscribed  rrSndni 
as  3  to  3.  A  sphere  is  said  to  be  inscribed  in  a  cylinder,  when 
its  diameter  is  equal  to  the  height  and  diameter  of  the  cylinder. 

The  volume  of  an  annular  I  is  equal  to  the  product 

of  its  section  into  the   mean  circumference.     We  have 
that  an  annular  torus  is  a  solid,  generate-! 
a  circle  about  an  axis,  situated  in  the  plane  of  the  circle, 
and  at  right  angles  U>  the  plane  of  revolution. 

radius  of  the  generating  circle,  and  r  the  i 
of  its  centre  from  the  axis,  we  have— 

\        «  R'  x  3«  r  =  19-73  R»  x  r. 


BOOK  OF   INDUSTRIAL  DESIGN. 


PROPORTIONAL  MEASUREMENTS  OF  THE   VARIOUS   PARTS  OF  AN   ENTIRE   ORDER. 
THE      (MODERN)      DORIC      ORDER. 


.J  i 


Cornice,  . 


Frieze, 


f  Reglet,  .  . 
Cavetto,   . 

Fillet,    .  . 

Cymatium, 

Corona,  . 
Fillet,  .  . 
Mutules,  . 
Guttte,  .  . 
Fillet,    .  . 


Cyinatium, 

Capitals  of  the  Triglyphs, 


.  (  Ta?nia, 

Architrave,-!  p    .    ' 

(  r  acia, 


Catital, 


Shaft,  . 


Base,.  . 


Cornice, 


Dado, 


Base,  . 


Reglet,  .  .  , 
Cymatium, . 


Abacus,    .... 
Echinus,  .... 

Three  Annulets, 

^  Necking,  .... 


Beading  or  Astragal, 
Cincture, 

Shaft  Proper,  .... 


Fillet,.  . 
Beading, 
Torus,  . 
Plinth,  . 


Reglet, 

Quarter-Round, 

Fillet, 

Corona,    .... 

Cymatium,  .  .  . 


Fillet, 

Beading, 

Cyma  Reversa,   .  .  . 

Plinth, 

Sub-Plinth  or  Socle, 


2 

<u 

2 

6 

2 

5 

a 

4A 

2 

2 

2 

l! 

1 

3 

1 

Oi 

iU 

n 

11* 


Total  height  of  the  Orde 


1      31 

1     3i 

1     2^ 

1     2 

1      1| 

111 

10| 

10" 

1     0 

m 

10" 
1     0 

i    U 

1  2 
1  5 
1     5 


1     11 

1  10| 
1     9| 


1     5 


2! 


2    '    1 

10     $    ' 


1 

u 

4 


M6     0 


13  10i 


2-833 
2.583 
2-542 
2-500 
2-417 
2-375 
2-167 
2-125 
1-250 
1-083 
1-042 
•959 
•917 

•833 

•959 
•833 


>    '     6 


4     0         4     0 


1-292 
1-271 
1-188 
1-167 
1-146 
•959 
•875 
•833 

1-000 
•959 
•833 

1-000 

1-104 
1-167 
1-417 
1-417 


1-917 
1-889 
1-806 
1-750 
1-542 
1-459 

1-417 


1-500 
1-583 
1-583 
1-708 
1-750 
1-792 


•083 

■250 

•042 

•125 

•333 
•042 

■     1-500 

•042 

■209 

■042 

•16G 

•ICG, 

1-500 

1-500 

•107 
•833 

.     1-000 

•042") 

•083 

•209 
■209 

■124 

•333 

•0S3 
•042 


•0831 
•083  I. 
•334  f 
■500  J 


4-000        4-000  I  16  000 


4       25  333 


. 


'.  IIUUUS    PART8   OF   AN    ENTIRE   ORDER. 


THE    T08C  A  ■     0  K  n  I  it. 


i  J  is.  M..Wn  ...I  M<xMi>f* 
—  bag  ik*  IW.J. 


Ttw  Mud.U  -  I. 


P 


Qujuiit-i: 

I !  



I  - 


Cymatium, 


A«CinT«ATX,  ■ 


fVU, 






R  •iiii.1, 






fAatngal, .  .  . 
stmft  Pi 


I 


linth. 


I  ' 

)  Cymatium, 


I  Socle  or  ninth, 


Total  baLgH  ..f  d    I 


a  3} 

1  111 

10 


m.  r. 

i 
1 


f  *  V 


■a 

'21 

1     0 

1  H 


II     0 


i  .  B 

•'.'17 
1000 

i  :r.:> 


i    fij 
1     8 


1     <■' 
1     - 


!    '} 


3     8 

'. 


i  881 

1  117 


i  :.  i -j 

l  :    I 


•333' 

. 

•333 

i  Iff] 

■181 

3600 


1-000 
•331  J 


11875 


•181  1 

I       -333  I 


117 


••  Ubln  we  tan  eaiuly  H. -tcmiinr  Im  prOfMf 
nMMimimt   for  any  member  <<r  monldiiig,  in   (I 

hen  the  height  of  d  Pot  tl,i. 


U  an  jlw.,  ih.  tnt  .n  I...  u  IS.  qrl»r  portm,  IS. 


hi  moat  t--  divided  by  the  decimal  • 
mi'iil  in  tin'  talili  «  lor  tin1  t"i  I   to  the 

i  .ill  of  the  module  proportioned  to  audi  height.     Tlicn 
that  of  any  required  i  I  by  multiplying  th  - 

into  the  decimal  in  tin-  ' 

II  It  ii  required  to  know  »  ' 


BOOK   OF   INDUSTRIAL  DESIGN. 


tin'  lower  part  of  the  shaft  according   to  the  Tuscan  order,  tho 

height  of  the  entire  order  being  15  feet. 

The  height  of  the  entire  order  being  22167  when  the  modulo 

'22-167 
=  1 .  we  have  — tt~ 

feet,  the  diameter  of  the  lower  part  of  the  shaft. 


=  1  -4778  the  module,  and  1  -4778  x  2  =  2-9556 


Second  Example. — What  is  the  height  of  the  socle  or  lowor 
plinth  according  to  the  Tuscan  order,  supposing  the  module  to  be 
1-4778  feet  ?     We  have  1-4778  x  -417  =  -616. 

In  like  manner  the  dimensions  of  all  the' other  details  may  bo 
easily  determined  according  to  tho  Tuscan  or  Doric  order. 


CHAPTER    in. 
ON  COLOURING  SECTIONS,  WITH  APPLICATIONS. 


CONVENTIONAL   COLOURS. 


127.  Hitherto  we  have  indicated  the  sectional  portions  of 
objects  by  means  of  linear  flat-tinting.  This  is  a  very  tedious 
process,  whilst  it  demands  a  large  amount  of  artistic  skill — only 
obtainable  by  long  practice — to  enable  the  draughtsman  to  pro- 
duce pleasing  and  regular  effects;  and  although,  by  varying  the 
strength  or  closeness  of  the  lines,  as  we  have  already  pointed  out, 
it  is  possible  to  express  approximately  the  nature  of  the  material, 
yet  the  extent  of  such  variation  is  extremely  limited,  and  the  dis- 
tinction it  gives  is  not  sufficiently  intelligible  for  all  purposes.  If, 
however,  in  place  of-such  line  sectioning,  we  substitute  colours 
laid  on  with  a  brush,  we  at  once  obtain  a  means  of  rapidly  tinting 
the  sectional  parts  of  an  object,  and  also  of  distinctly  pointing 
out  the  nature  of  the  materials  of  which  it  is  composed,  however 
numerous  and  varied  such  materials  may  be.  Such  colours  are 
generally  adopted  in  geometrical  drawings;  they  are  conventional 
— that  is,  certain  colours  are  generally  understood  to  indicate  par- 
ticular materials. 

In  Plate  X.  we  give  examples  of  the  principal  materials  in  use, 
with  their  several  distinctive  colours;  such  as  stone  and  brick,  steel 
and  cast-iron,  copper  and  brass,  wood  and  leather.  Wo  propose 
now  to  enter  into  some  details  of  the  composition  of  the  various 
colours  given  in  this  plate. 


THE  COMPOSITION  OR  MIXTURE  OF  COLOURS. 
PLATE  X. 

128.  Stone. — Fig.  1.  This  material  is  represented  by  a  light  dull 
yellow,  which  is  obtained  from  Roman  ochre,  with  a  trifling  addi- 
ton  of  China  ink. 

129.  Brick. — Fig.  2.  A  light  red  is  employed  for  this  material, 
and  may  be  obtained  from  vermilion,  which  may  sometimes  be 
brightened  by  the  addition  of  a  little  carmine.  A  pigment  found 
in  most  colour-boxes,  and  termed  Light  Red,  may  also  be  used  when 
great  purity  and  brightness  of  tint  is  not  wanted.  If  it  is  desired 
to  distinguish  firebrick  from  the  ordinary  kind,  since  the  former  is 
lighter  in  colour  and  inclined  to  yellow,  some  gamboge  must  be 
mixed  with  the  vermilion,  tho  whole  being  laid  on  more  faintly. 
In  external  views  it  is  customary  to  indicate  the  outlines  of  the 
individual  bricks,  but  in  the  section  of  a  mass  of  brickwork  this 
"efinement  may  be  dispensed  with,  except  in  cases  where  it  is 


intended  to  show  the  disposition  or  method  of  building  up.  Thus, 
in  furnaces,  as  also  in  other  structures,  the  strength  depends  greatly 
on  the  method  of  laying  the  bricks.  When  vermilion  is  used  in 
combination  with  other  colours,  the  colour  should  be  constantly 
mixed  up  by  tho  brush — as,  from  its  greater  weight,  the  vermilion 
has  a  tendency  to  sink  and  separate  itself  from  the  others;  and  if 
this  is  overlooked,  a  varying  tint  of  unpleasing  effect  will  he 
imparted  to  tho  object  coloured. 

130.  Steel  or  Wrought  Iron. — Fig.  3.  The  colour  by  which  these, 
metals  are  expressed  is  obtained  from  pure  Prussian  blue  laid  on 
light — being  lighter  and  perhaps  brighter  for  steel  than  fi  >r  wrought- 
iron.  The  Prussian  blue  generally  met  with  in  cakes  has  a  con- 
siderable inclination  to  a  greenish  hue,  arising  from  the  gum  with 
which  it  is  made  up.  This  defect  may  be  considerably  amended 
by  the  addition  of  a  little  carmine  or  crimson  lake — the  proper 
proportion  depending  on  the  taste  of  the  artist. 

131.  Cast-iron. — Indigo  is  tho  colour  employed  for  this  metal  ; 
the  addition  of  a  little  carmine  improves  it.  The  colours  termed 
Neutral  Tint,  or  Payne's  Gray,  are  frequentl]  used  in  place  of  the 
above,  and  need  no  further  mixture.  They  are  not,  however,  30 
easy  to  work  with,  and  do  not  produce  so  equable  a  tint. 

132.  Lead  and  Tin  are  represented  by  similar  means,  the 
colour  being  rendered  more  dull  and  gray  by  the  addition  of  China 
ink  and  carmine  or  lake. 

133.  Copper. — Fig.  5.  Fortius  metal,  pure  carmine  or  crimson 
lake  is  proper.  A  more  exact  imitation  of  the  reality  may  be  ob- 
tained by  the  mixture,  with  either  of  these  colours,  of  a  little  China 
ink  or  burnt  sienna — the  carmine  or  lake,  of  course,  considerably 
predominating. 

134.  Brass  or  Bronze. — Fig.  6.  These  arc  expressed  by  an  orange 
colour,  the  former  being  the  brighter  of  the  two;  burnt  Roman 
ochre  is  the  simplest  pigment  for  producing  this  colour.  Where, 
however,  a  very  bright  tint  is  desired,  a  mixture  should  be  made 
of  gamboge  with  a  little  vermilion— care  being  taken  to  keep  it 
constantly  agitated,  as  before  recommended.  Mam  draughtsmen 
use  simple  gamboge  or  other  yellow. 

135. —  Wood. — Fig.  7.  It  will  bo  observable,  from  preceding 
examples,  that  the  tints  havo  been  chosen  with  reference  to  the 
actual  colours  of  the  materials  which  they  are  intended  to  express — 
earning  out  the  same  principle,  we  should  have  a  very  wide  range 
in   the  case  of  wood.     Tho   colour  generally  used,  however,  is 


burnt  •  irpth  oratreogth  wit' 

■at*  be  cofcj.i.  -ual   to  epidy 

•hade   first,  aubacqoently  showing   the   graining  with  a 

with  burnt  «i.-nn».     Throe  poinU  are  »u«- 

it  variation,  and  very  mock  mu»t  be  left  to  the 

ju'l^rirtit  of  it- 

/  I  Jut-Rubber,  and   Gutta   Perrha. — 

. 

r.ha  by  dark   •  I  india- 

■ 

V.  -  a  little 

i  at  readineaa  am!  facility  tlion  if  hi* 

'       ir«. — Wo  hnve  aeen  by  what 

•i.     It  tnay  In-  imagined  (hat 
.1  is  ai.  .  — t li:it  ia,  limply 

itjon   t..  the  fi 
i  lent  may  tl. 

.  id  which  >t  i .. 

■ 
quired  quantity 

dour  in 

■    ■ 

■••.  !i'.  Ii  it 
fl  i  tint,  it  i->  will  to  | 

• 

Wly  obtain  tl, 

applied 
When  the  di 

ir  Will, 

■uall  ', 

■  I  t.i  fill 
.'  in ii-:  !-■   r.  |   ■ 

It 

I  '  it  will 
It    la   a    vii,  .1    with 

I 

rath  be 


a  fine  eveo  ahade,  for  the  leaftt  quantity  of  aaliva  which  may  be 

taki  ti  uj,  by  th«-  l.r.i.h  baa  the  i  rT.v  ..:id  altogether 

apnilne;  the  wmah  of  I 

cleanly  method,  the  artiat  should  have  a  piece  of  bl 

Ui  ride— (kt  bom  abaorbeal  Km  better.     Bj  paerief  th,    break 

I  .   u*  colour  DM  ''  and  a»  line  a 

ua.     The  bru-1 
paaaed  i  -.urn-  [art  of  Un 

try;  ai.d  when  th<-  Wniiiiiati..n   of  a  large  ahade  ia 
■ 
,    be  left  dark.-r  at  tliat  \<ur- 
idwuld   In-  taki-n  to  ki.p  i  \artlv  t..  tl..-  ..inline;   and  ai 
..-.  Ji"u!.l  Ih-  wbollj 

•  mark  at  Ike  jun.-ti..n  of  tin-  tWO  |»Tti..n«.    Finally, 

I  ii, .1  l« 
id  the  colour  should  li 
for  th. 

tin-  better  r. -nil  of  the  «..rL.  undei 


CONTINUATION  OF  THE  BTJ  l>\   I  >!'  PROJECTIONa 

lin.  i  - 

TI.MK    XI. 

i       \'.  -.  ihown,  whi  • 

\  ill.,  thai    '  or  cut 

► 
'  \\i:b  th.  Plate  XL, 

tli.it  in  ; 

* 
- 

be  divided  by  ■ 
dona]  < 

.1.  j  t)i   of   tl  u  alao  th.- 

r  ;   lhir.il  . 

Thai 


BOOK  OF   INDUSTRIAL  DESIGN. 


centre-bit,  which,  of  course,  should  not  turn  with  the  spindle-foot, 
is  prevented  from  doing  so  by  means  of  the  key,  c,  which  fits 

into  a  cross  groove  in  its  under  side,  the  key  itself  being'  held 
firmly  by  the  grooves,  b,  into  which  its  projecting  ends  are  made 
to  tit.  Of  these  details,  the  cup-piece,  A,  is  of  east-iron,  the 
footstep,  B,  of  gun-metal  or  brass,  the  centre-piece,  c,  of  tempered 
Steel,  and  the  small  key,  c,  of  WTOUght-iron.  Therefore,  bearing 
in  mind  what  lias  already  been  said,  we  may  indicate  these  various 
materials  in  the  sections,  either  by  line-shading,  of  different 
strengths,  as  in  the  figure,  or  by  means  of  colours,  corresponding 
to  those  employed  in  Plate  X.;  and  we  may  here  remark,  that 
where  line-sectioning  is  used,  brass,  guh-mctal,  or  bronze,  is 
frequently  expressed  by  a  series  of  lines,  which  are  alternately 
full  and  dotted.  There  are,  besides,  many  ways  of  varying  the 
effect  produced  by  line-shading.  For  example,  the  spaces  between 
the  lines  may  be  alternately  of  different  widths,  or  the  lines  may 
be  alternately  of  different  strengths. 

Strictly  speaking,  figs.  1  and  1*  are  all  that  are  necessary  for 
the  representation  of  the  object  under  discussion.  The  cup- 
piece,  a,  however,  which  is  externally  cylindrical,  has,  at  four 
points,  diametrically  opposite  to  each  other,  certain  projecting 
rectangular  plane  surfaces,  d,  which  are  provided  to  receive  the 
thrust  of  the  screws  which  adjust  the  footstep  accurately  in  the 
centre.  The  width  of  these  facets  is  shown  in  the  plan,  fig.  1 
whilst  then  depth  is  obtainable  from  the  elevation,  fig.  1".  If, 
instead  of  these  facets,  d,  being,  as  they  are,  tangential  to  the 
cylinder,  a,  they  had  projected,  in  the  least,  at  their  centres,  then 
depth  would  necessarily  have  been  given  in  the  section,  fig.  Is, 
and  in  such  case  the  elevation,  fig.  1",  might  have  been  altogether 
dispensed  with.  Whilst  referring  to  the  representation  of  the 
•projecting  facets,  in  connection  with  the  cylinder,  a,  we  may 
remark,  that  when  a  cylinder  is  intersected  by  a  plane,  which  is 
parallel  to  its  axis,  the  fine  of  intersection  is  always  a  straight 
line,  as  efi  figs.  1  and  1". 

140.  Stuffing-box  cover,  or  gland. — In  pumps  and  steam-engine 
cylinders,  the  cover  is  furnished,  at  the  opening  through  which 
the  piston-rod  passes,  with  a  stuffing-box,  to  prevent  leakage. 
The  hemp,  or  other  material  used  as  packing,  is  contained  in  an 
enlargement  of  the  piston-rod  passage,  and  is  tightly  pressed  down 
by  a  species  of  hollow  bush  with  flanges,  as  reoresented  in  plan 
in  fig.  2,  and  in  elevation  in  fig.  2".  In  this  instance,  the  neces- 
sity of  a  sectional  view  is  still  more  obvious  than  in  the  case  of 
the  footstep  already  treated  of.  In  the  vertical  section,  fig.  2*, 
it  is  shown,  that  the  internal  diameter  is  not  uniform  throughout, 
and  that  there  is  a  ring  or  ferule,  b',  let  in  at  the  lower  part  of 
the  interior.  The  cylindrical  opening,  a,  of  the  gland,  coincides 
exactly  with  the  diameter  of  the  piston-rod  :  the  internal  diameter 
of  a  portion,  b,  of  the  ring,  e\  is  also  the  same.  -The  part,  e, 
however,  comprised  between  these  two,  is  greater  in  diameter,  so 
as  to  lessen  the  extent  of  surface  in  frictions]  contact  with  the 
piston-rod,  and  it  also  serves  for.  the  lodgment  of  lubricating 
mailer.  It  is  further  discernible  in  the  section,  that  the  flanges 
or  lugs,  <l,  which  project  on  either  side  of  the  upper  portion  of  the 
gland,  have  each  a  cylindrical  opening,  e,  throughout  their  whole 
depth.  These  are  the  holes  fur  the  bolts,  which  force  down  the 
gland,  and  secure  it'to  the  corresponding  flanges,  or  lugs,  on  the 


Btuffing-b6x.  The  annular  hollowing  out,  /,  at  the  upper  and 
internal  part,  of  the  gland,  acts  as  a  reservoir,  into  which  llio 
lubricating  oil  is  first  poured,  and  whence  it  gradually  oozes  ItO 
tho  interior.  The  ring,  b',  is  forcibly  fitted  into  the  bottom 
the  gland,  and  terminates  below  in  a  Wedge,  in  lie-  same  manner 
as  the  gland  itself,  the  double  Wedge  jamming  the  packing  against 
the  piston-rod  and  the  sides  of  the  Stuffing-box,  and  thus  forming 
a  steam-tight  joint.  The  ring,  B',  is  generally  made  of  brass, 
both  with  a  view  to  lessen  the  friction,  ami  to  iis  being 
with  facility  when  worn,  without  the  necessity  of  renewing  the 
whole  gland.  The  latter  is  generally  made  of  cast-iron,  though 
the  whole  is  sometimes  made  of  brass  or  jjuii-hh ital. 

141.  Spherical  Joint. — In  some  cases,  a  locomotive  receives  water 
from  its  tender  by  means  of  pipes  which  are  tilted  with  spherical 
joints,  as  a  considerable  play  is  necessary  in  consequence  of  the 
engine  and  tender  not  being  rigidly  connected  together,  and 
obviate  any  difficulty  of  attachment  from  the  pipes  in  the  locomo- 
tive not  being  exactly  opposite  to  those  in  the  tender,    'i'lii- 
of  joint,  represented  in  plan  and  elevation  in  tigs.  3  and  3',  gives 
a  free  passage  to  the  water,  in  whatever  position,  within  <    I 
limits,  one  part  may  be  with  respect  to  the  other.     For  its  con- 
struction to  be  thoroughly  understood,  tin-  vertical  section  fig.  3'  is 
needed.     This  view,  indeed,  at  once  explains  the  various  i 
nent  parts,  consisting  — first,  of  a  hollow  sphere,  a,  of  i|;, 
thickness  as  the  pipe,  b,  of  which  it  forms  the  prolongation  ;  ami, 
second,  of  two  hemispherical  sockets,  C,  D,  which  embrace  tho  ball. 

a,  and  which  are  firmly  held  together  by  bolts  passing  through 

lugs,  a,  a.     When  this  species  of  joint  is  used  of  a  small    i 
the  junction  of  a  gas  chandelier  with  the  ceiling,  the  two  half- 
sockets  are  simply  screwed  together — this  method,  indee 
adopted  in  many  locomotives.     It  must  be  borne  in  mind,  that  our 

object  in  this  work  is  simply  to  instruct  the  student  to  i [irately 

represent  mechanical  and  other  objects,  and  for  this  purpi 
employ  both  precept  and   example;    but  such  examples  do  not 
necessarily  comprise   tho   latest  and   most    improved  or  efficient 
forms.     The  half-socket,  c,  forms  part  of  the   continuation,  s,  of 
the  feed-pipe,  whilst  the  half-socket,  d,  is  a  detached  piece,  neces- 
sarily moveable,  to  allow  of  the  introduction  of  the  sphcri 
A.     This  half-socket,  D,  is  partially  cut   away  at  the   lower  part, 
and  does  not  fit  closely  to  the  neck  of  the  ball.      This  aih.ws  t lit: 
pipe,  b,  to  move  to  a  slight  extent  from  side  to  side  in  anydu 
and  flic  upper  end  of  the  ball,  a,  is  cut   away  to  a  corresponding 
extent,  to  prevent  any  diminution   of  the   Opening  in 
when  the  two  portions  are  thus  inclined  to  each  other.     The  pipe, 
e,  with  its  half-socket,  c,  is  an  example  of  the  combination  of  a 
cylinder  with  a  sphere,  and  gives  us  occasion  thai  the 

intersection   formed  by  the   meeting  or  junction   of  these  solids  is 
always  a  circle   in   one   projection,  and  a  straight   line  in  the  Other. 

The  subject  of  such  intersections  will  be  discussed  more  in  detail 

in  reference  to  Plate  XIV. 

The  sockets,  r  and  n,  are  formed  with  four  external  lugs,  or  eye- 
pieces. </.  for  connection  by  bolts,  as  before  stated.  The 
outlines  of  these  logs,  which  glide  tangentiolly  into  that  of  the 

ho.lv  of  the  socket,  give   rise   to  the  solution   OI  a   problem  which 

ni.e.   lie  thus  put  :    To  draw  with  a  given  radius  an  arc  tangential  In 

n  arcs.     The  solution  is  thus  obtained:  with  the  centres 


Tin:   i  nu\i(iHT 


s 

i  «.f  the 

and  ti-.-iK.tjil  .. 

•  *>ure  gauge*, 

■ 
to  the  Mcam  aa  soon  a-  pro  ore  tlian  i 

deUrsained  oa  lad  for  whioh  the  valre  la  loaded.     I' _-    I    I*,  and 

..Ii J  \l-r- 

th-al  aertion  of  a  aafi 

eonaSatx  a,  jur- 

Banantl] 

ivm  and 

!.  at  ill.- 

n  in  an 

- 

■•\;lh  tliat   c.f  ifae  latt.  r.     Tl»-  upper 

■ 

•mil  the 
■ 
and  lb 

/  I  ■  \ 

net  with  In  Cornwall, 
a*  mar,' 

1he    atnun,   with   a   \.ry  lit:! 
I 

I 
.    and    a    loll- 
with  a  r  ■ 

!  when  it  i«  li!' 
art-    nimultan. 


•nil  |urt  of  l!  -  tpimlte 

in  .-tn-  with  i! 
..:.,-!..-.  c.     The  seal  U  anmU 
ihre  pmeota  a 

: 

i  the  curird  junction  ff  tKr  body  •  •/ 

.1/  ;«n\     Ti 
of  in  r.  :  -    drawn 

1  of  tiu>  branch,  c  with  the  1 

as,  an.1  passing 
-jinple: 

and  the 

1  \\  liii-h   tlv  an 

- 

the  ajv 

it,  a,  an-  drawi. 

ajul  act  nee  alw) 

ti'-n  will   show  llut   t! 

■ 

external  outline. 

nt  who  ha*  a 
III. 


SIMPLE    APPUCATfi 

run:  xu. 
111.  l 

and  wood,  arc 
Ok,  and 

in  all  m 

■ 
\  ■ 

•  the  main 
.  ■    u  lanla^u 

than  cast,  and  of  possessing  g 

1  ij    w  I  V  p    l,  1.  :>.  ■  I  •  Bflnrcol 


BOOK  OF  INDUSTRIAL  DESiGN. 


projections  of  a  wooden  shaft,  such  as  is  used  for  a  water-wheel. 
Fig.  4  shows,  on  one  side,  a  lateral  elevation  of  the  shaft,  furnished 
with  its  iron  ferules  or  collars,  and  its  spindle ;  and  at  the  same 
time,  on  the  other  side,  a  vertical  section,  passing  through  the 
centre  of  the  shaft,  giving  the  ferules  in  section,  but  supposing 
the  central  spindle,  with  its  feathers,  to  be  in  external  elevation. 
Generally,  in  longitudinal  sections  of  objects  enclosing  one  or  more 
pieces,  the  innermost  or  central  piece  should  not  be  sectioned, 
unless  it  has  some  internal  peculiarity — the  object  of  a  section  be- 
ing to  show  and  explain  such  peculiarity  where  it  exists,  and  being 
quite  unnecessary  where  the  object  is  simply  solid.  In  the  same 
manner,  it  is  not  worth  while  sectioning  the  various  minutiae  of 
machinery,  such  as  bolts  and  nuts,  simple  cylindrical  shafts  and 
rods  and  screws,  unless  these  are  constructed  with  some  intrinsic 
peculiarity. 

Fig.  5  is  a  transverse  section  through  the  middle  of  the  shaft, 
and  merely  shows  that  it  is  solid,  and  that  it  lias  the  external  con- 
tour of  a  regular  octagon.  Fig.  6  is  an  end  view  of  the  same 
shaft,  showing  the  fitting  of  the  spindle,  with  its  feathers,  into  the 
socket  and  grooves,  funned  in  the  end  of  the  shaft  to  receive 
them,  and  the  binding  of  the  whole  together  by  the  ferules  or 
hoops.  These  views  are  what  are  required  to  determine  all  the 
various  parts  of  the  shaft.  It  manifestly  consists,  in  fact,  of  a 
long  prismatic  beam  of  oak,  A,  of  an  octagonal  section,  and  of 
which  the  extremities,  b,  are  rounded,  and  slightly  conical.  The 
spindles,  B,  which  are  let  into  the  ends,  are  each  cast  with  four 
feathers,  c,  and  a  long  tail-piece,  d,  uniting  and  strengthening 
them.  Some  engineers  construct  the  spindles  without  the  addi- 
tional tail-piece,  d.  Though  this  simplifies  the  thing  considerably, 
it  is  an  arrangement  which  does  not  possess  so  much  strength  as 
when  the  spindle  is  longer.  The  beam-ends  are  turned  out  and 
grooved  to  receive  these  spindles,  the  grooves  for  the  feathers 
being  made  rather  wider  than  the  feathers  themselves.  When 
the  spindles  are  introduced  into  the  sockets,  b,  thus  formed  for 
them,  the  whole  are  bound  together  by  means  of  the  iron  hoops, 
f,  which  are  forced  on  whilst  hot.  After  this,  hard  wooden 
wedges  are  jammed  in  on  each  side  of  the  feathers,  thus  tightening 
and  solidifying  the  whole  mass.  In  addition  to  this,  iron  spikes, 
g,  are  sometimes  hammered  in,  to  jam  up  the  fibres  of  the  wood 
still  closer.  Fig.  1,  which  is  a  shaded  and  finished  elevation  of 
one  end  of  the  shaft,  gives  an  accurate  idea  of  its  appearance  when 
complete  and  ready  for  adjustment. 

146.  Cast-iron  Shaft. — There  are  several  descriptions  of  cast- 
iron  shafts.  Some  are  cast  hollow,  others  quite  solid,  and  cylin- 
drical or  prismatical  in  cross  section.  Such  as  are  intended  to 
sustain  very  great  strains,  are  generally  strengthened  by  the  addi- 
tion of  feathers,  which  project  more  towards  the  middle.  These 
give  great  rigidity  to  the  piece.  A  shaft  of  this  description  is 
represented  in  elevation  in  fig.  7,  half  being  sectioned  through  the 
irregular  line,  1 — 2 — 3 — 4,  and  half  in  external  elevation.  Fig.  8 
is  an  end-view  of  it ;  and  fig.  9  a  transverse  section  through  the 
line,  5 — 6,  in  fig.  7.  In  practice,  it  is  not  considered  absolutely 
necessary  that  a  section  should  follow  a  straight  line.  Frequently 
a  much  greater  amount  of  explanation  may  be  given  in  one  view, 
by  supposing  the  object  sectioned  by  portions  of  planes  at  differ- 
ent parts,  and  solid  and,  easily  comprehended  portions  are  generally 


shown  in  elevation,  as  the  feathers  of  the  shaft,  in  the  present  in- 
stance, or  the  spokes  of  a  spur-wheel  or  pulley.  The  shaft  under 
consideration  is  SUeh  a  one  as  is  employed  for  hydraulic  motors. 
The  body,  a,  is  cylindrical  and  hollow,  and  it  is  cast  with  four 
feathers,  b,  disposed  at  right  angles  to  each  other,  and  of  an  ex- 
ternal parabolic  outline,  so  as  to  present  an  equal  resistance  to 
torsion  and  flexure  throughout.  Near  the  extremities  of  these 
feathers,  four  projections  are  cast,  for  the  attachment  of  the  bosses 
of  the  water-wheel.  These  projections  are  formed  with  facets, 
so  as  to  form  the  corners  of  a  circumscribing  square,  as  shown  in 
fig.  8;  and  they  are  planed  to  receive  the  keys,  i,  by  which  they 
are  fixed  and  adjusted  to  the  bosses  or  naves,  which  are  grooved 
at  the  proper  places  to  receive  them.  The  spindles,  n,  which 
terminate  the  shaft  at  each  end,  are  cast  with  it,  and  are  afterwards 
finished  by  turning.  The  shaft  thus  consists  of  only  one  piece,  or 
casting. 

147.  Although  we  have  already  shown  tho  method  of  drawing  a 
parabola,  in  Plate  V.,  the  outline  of  tho  shaft  feathers  affords  a 
practical  exemplification,  which  it  will  be  useful  to  illustrate.  We 
here  also  give  the  method  generally  adopted — because  of  its  sim- 
plicity— when  the  curve  is  a  very  slow  or  obtuse  one,  such  as  is 
given  to  the  feathers  of  shafts,  beams,  side-levers,  connecting-rods, 
and  similar  pieces.  It  is  understood,  in  these  cases,  that  two  points 
in  the  curve  are  given;  the  one,  a,  fig.  7,  being  at  the  summit, 
and  at  the  same  time  in  the  middle  of  the  piece,  and  the  Other,  A, 
situated  at  the  extremity.  In  the  present  instance,  wo  suppose 
the  heights,  a  c  and  b  d,  from  the  axial  line,  m  n,  of  the  shaft  to  be 
given.  This  line,  mn,  may  also  be  taken  as  the  centre  line  of  a 
beam,  or  connecting-rod.  After  having  drawn  through  the  point, 
b,  a  line,  e  b,  parallel  to  the  axis,  divide  tho  perpendicular,  a  e,  into 
any  number  of  equal  parts,  and  transfer  these  divisions  to  the  line, 
hi,  the  prolongation  of  the  line,  db;  then  draw  lines  from  the 
points,  1,  2,  3,  to  the  summit,  a.  Further,  divide  also  the  length, 
cd,  into  the  same  number  of  equal  parts  as  the  perpendicular, 
and,  through  the  divisions,  1',  2/  3',  draw  other  perpendiculars, 
the  respective  points,/, g,  h,  of  intersection  of  these  with  the  lines 
already  drawn,  will  bo  points  in  the  required  curve.  As  the 
lower  feather  is  an  exact  counterpart  of  the  upper  one.  the  perpen- 
diculars may  be  prolonged  downwards,  and  corresponding  di 

as  1'— /',  2'— <g',  3 — h',  set  off  on  them.  To  draw,  also,  the  '<■  If 
of  each  feather  to  the  left,  it  is  merely  necessary  to  erect  perpen- 
diculars of  corresponding  lengths,  at  corresponding  points  ill  the 
axis.  A  ditferent  method  of  drawing  this  curve  is  sometimes 
adopted;  namely,  the  one  which  we  have  already  given  in  Plate 
IX.,  for  the  entasis  of  the  Tuscan  column.  As,  however,  it  does 
not  possess  the  advantages  of  the  true  parabolic  form,  and  as  tho 
curve  becomes  too  sudden  towards  the  extremities,  we  think  the 
method  given  in  Plate  XII.  is  to  be  preferred. 

Fig.  3  represents  a  portion  of  the  shaft  just  discussed,  shaded 
and  finished,  the  lines  running  in  ditferent  directions,  the  better  to 
distinguish  the  flat  from  the  round  surfaces. 

148.  Shaft  Coupling. — In  extensive  factories,  and  other  works, 
where  considerable  lengths  of  shafting  are  necessary,  thej  bave 
to  be  constructed  in  several  pieces,  and  coupled  together.  These 
couplings  are  generally  of  cast-iron,  and  formed  of  one  or  moro 
pieces,  according  to  their  size.     One  form  consists  of  a  species  or" 


. 


cjfodnual   »«**t,   arcurstely   turned    bteraaDy,   which   receive* 
the  rod>  of  i!m*  two  shaft*  to  beVoutccted,  these  being  scarfed  or 
htt*  ana  other,  *e  a*  to  be  bound  wail  together,  and  re- 
volve like  om  coatianoaa  piece.     According  to  another  form,  two 
ire  employed,  of  increased  diameter  at  the  part  wV-re  they 
and   at   this    part   into   quadrant-ehaped   dutches, 
-.     The  coupling  repreaented  in  aid. 
i  kind  ;  and  in  front  elevation,  a*  separated, 

,  ,.upling  waa  designed  for  a  shaft,  of  w  hi.-h  the  diameter 
at  the  collar*  waa  88  centimetre*.    The  sock 
is  adjusted  on  the  end  of  the  first  part  of  the  shaft,  c     T 

»',  b  similarly  adjusted  on  the  end 
of  ti..-   >!iaft.    The**    •■        -■       -|iooea  gear  »i!i   each   otfcsr, 

■  ..-ans  of  the  projection*  or  . 

•  and  »'.  c  •!.-  tit  the 

one  into  the  I 

■  .  A,  shows  the 
exact  ahape  and  dimensions  of  theae  projecting  dutches,  each 
...'  a  quadrant  of  the  circle  on  the  face  of  the  socket-piece. 
Those  of  the  second  |*vce,  a',  are  precisely  the  same,  or. 
"-«  on   a,  au  tliat  1  - 
-,  as  shown 
accnrati 

shafting  is  obtained,  in  the  first  place,  by  means  •■' 
diamctr  '.  and  let  half  into  the  shaft, 

and  hal; 

.ludiual 
j  ;  «ling. 

nix  a:  vs  a  woode*   model  or  rArrtta 

or  i 

■  nny  piece  of  mechanism  which  it  is 

'    - 
.  ■ 

- 
•nsiderable  sU  rt   of  th» 

as  also  a  knowlisl^e  of  the  >. 
piupilati 

■ 

etjaanaaah      BatNd ,  however,   plane-tree   or   sreun   r.-   ..r   i...k 

b  u~-J  ;  and  fur  small  patterns,  and  -  _Tvat  precision, 

mabog>  i  u*ed,  it 

ehouM  ry,  and  well  seasoned.     The  pattern  ia  made 

■  according  to  the  dimensions  of  the 

Lance,  a  column  of  any  eonaiderahle 

-   far  a  coupling  of  large  ,aUe, 

aoch  aa  that  rcpro*  and  14,  the  pattern  ia 

•  ing  the 
up,  there  ia  leaa  ri»k  of  warp- 

upling-pioc*  ia  represented.  ; 
nal  aide  elevation,  and  partly  in  longitudinal  section,  bein  | 


through  the  axis.     rV   1 J  is  ■ 
elevation,  ebowing  the  project. 

ti].— • »..  a-  Ihal  lb*  path  nj  a  hraMal  >>t  ta  •  i--*.-<iv  ■  ay,  maad 
the  circumference*  of  which  a- 

aa  atare*  i*  li 
up  into  piece*  of  the  repaired  thirlmei,  and  the  aide*  an 

il,  to  coincide  with  the  radii,  cd.cr.Uf. 
then  fitted  to  the  board*,  t>  n',  and  at  this  stage  present  the  ap- 
pearance of  the  left-hand  aort  The  drum  .- 
ward*  put  int..  the  lithe,  and  the  circumference  ia  rcdu  - 
a]  surface,  like  the  right-hand  portion  of  the  aame  I 
On  one  of  the  ends,  D,  of  thia  drum,  i-  jrcting 
clutch-piece,  a,  whirh  baa  U  •                                       of  a  board  of 
>.  mi  v  in  present  the  outline  of  fig.  li    On  the 

.'.  are  turned  down  to  a  di~  ..le  to 

Ihhi  in  the  coupting- 
'. 

-  lirface  aa  amooth  as  poaaibla, 
•    loam  of  which  the  mould  is 

-.  particularly  when  of  small  size,  are  more- 
ii    I4ack-lcad.  ■    polish 

and  hardness  to  the  surface.     The  diameter  of  the  con  -. 
ia  leaa  than  thai 

-'me  margin  in  the  casting  for  turning  and  grinding 
down  i  iirncnaiona.     The  oor> 

-  of  loam  placed  in  the  centre 

structed  on  end,  and   I  ■  d  not  require 

further  -  or  placed  in  a 

horizontal  poatfaa,  it  require*  to  be  aupported  at  both  end*,  and, 

•rengtheoed  by  wires  or  roda  pnakg  throegfa  iu 

■  .is  reason,  a  core-piece,  aa  r,  is  only  attached  to 

I    of  the  drum.     It  will   be  observed  that  this  ia  slightly 

..m  is  so  also,  but  to  a  leas  extent ;  the  core  itself, 

driest. 

J   Shjusk,  or  AOmtmet  f 
traction-  -fted  from  the  mould 

essary  to  form 
Ha  aides  with  a  alight  tap**,  or  dram,  a*  it  is  technical , . 

-.-piece,  r,  aa  Well  a»  that  of 
the  drum  itself,  must  be  less  at  the  lower  extremity,  or  at  the  part 
Lrodoced  into  the  mould,  than  at  the  opp  • 

.. .Terence  of  diameter  i*  euff;  |Hi*e. 

-.n.  as  b  the  case  with  all  the  metal*  of  the  engio.  • 

leaa  bulk  when  culd  than  w  hen  in  a  atate  of  fusion,  and,  bam  an)     : 

.Le  the  patterns  of  somewhat 

i.ineniions  than  the  resting  ia  to   be  when   finished.     It 

•hen.  tluit  when  the  pieces  to  be  cast  bare  afterward*  to 

be  planed,  tamed,  ground,  or  grooved,  it  is  necessary  to  bear  in 

in::..!,  in  Mnaatiajeling  lb*  wonrlw  asttara,  not  oal]  the  ati.  r  •• - 

itraction.  or,  as  it  is  termed,  the  *k 
the  metal,  but  also  that  which  is  occasioned  by  the  rednring  pnv 
eaaats  umdved    in   finishing  the  article.      In   general,  § 
require*  an  allowance  for  ahrink  of  from  1#:  L.;  «r*ii» 


BOOK   OF    INDUSTRIAL   DESIGN. 


iron,  however,  requires  a  much  larger  allowance.  The  allowance 
to  be  made  for  the  reduction  caused  by  tho  finishing  processes, 
depends  entirely  on  their  nature. 

When,  with  a  view  to  avoid  tho  expense  of  constructing  a 
pattern,  the  mould  is  formed  from  the  actual  object  which  is  to  bo 
reproduced  or  multiplied,  the  mould-makers  obtain  the  necessary 
margin  by  shifting  tho  model  slightly  during  the  formation  of  tho 
mould.  This,  of  course,  can  only  be  done  with  advantage  when 
tho  piece  is  not  of  intricate  shape. 


ELEMENTARY     APPLICATIONS 

RAILS   AND    CHAIKS   FOR    RAILWAYS. 
PLATE   XIII. 

151.  In  railways,  the  two  iron  rails  on  which  the  trains  run  are 
placed  at  the  distance  apart,  or  gauge,  of  lj  metres,  and  are 
generally  formed  of  lengths  of  4|  to  5  metres.  In  England,  the 
gauge  is  generally  4  feet  84  inches,  and  the  rails  are  rolled  in 
lengths  of  from  12  to  15  feet.  These  rails  are  supported  by 
cast-iron  chairs,  placed  at  from  9  to  10  decimetres  asunder,  and 
adjusted  and  bolted  on  oak  sleepers,  lying  across  the  rails,  imbed- 
ded even  with  the  surface.  Those  chairs  which  occur  at  the 
junctions  of  the  lengths  of  rails  are  made  wider  at  the  base,  and 
of  greater  length,  so  as  to  embrace  the  end  of  each  length  of  rail, 
and  render  their  rectilinear  adjustment  and  union  as  perfect  as 
possible. 

In  Plate  XIII.  we  give  details  of  a  very  common  form  of  rail  and 
chair.  There  arc  many  different  forms  in  use ;  but  the  method  of 
drawing  or  designing  each  will  be  similar,  and  may  be  thoroughly 
understood  from  the  exemplification  here  given.  Figs.  1  and  2 
represent  the  elevation  and  plan  of  a  chair,  with  a  portion  of 
the  rail  which  it  supports.  Fig.  3  is  a  vertical  section  through 
the  line,  1 — 2.  in  the  plan;  but  supposing  the  chair  to  be  turned 
round,  or  to  belong  to  the  right-hand  rail — showing,  in  connexion 
with  fig.  1,  the  relative  positions  of  the  two  lines  of  rails,  with 
their  respective  chairs.  Fig.  4  is  a  side  view  of  the  chair  alone, and 
fig.  5  is  an  end  view  of  a  length  of  rail.  This  chair,  which  is  de- 
signed with  the  view  of  combining  solidity  and  strength  with 
economy  of  material,  consists  of  a  wide  base,  a,  by  which  it  is 
seated  on  the  sleeper,  and  of  two  lateral  jaws,  B,  b',  strengthened 
by  double  feathers,  c,  c'.  The  base,  B,  is  perforated  at  a — the 
holes  being  cylindrical,  and  slightly  rounded  at  their  upper  edges. 
These  holes  are  for  the  reception  of  the  bolts  which  secure  the 
chair  to  the  sleeper.  The  space  between  the  jaws  of  the  chair  is 
for  the  reception  of  the  rail,  D,  and  the  wooden  wedge,  E,  which 
holds  it  in  position. 

In  this  example,  the  vertical  section  of  the  rail,  D,  presents  an 
outline  which  is  symmetrica]  with  reference  both  to  the  vertical 
centre  line,  be,  and  also  to  the  horizontal  line,  de,  fig.  5.  This 
permits  of  the  rail  being  turned  when  one  of  the  running  surfaces 
is  worn.  The  section  of  the  wedge,  e,  is  also  symmetrical  with 
reference  to  Its  diagonals,  so  that  it  is  immaterial  which  way  it 
is  introduced,  whilst  it  also  fits  equally  well  to  the  rail  when  the 
latter  is  reversed. 


Tho  outline  of  tho  rail  is  composed  of  Btraigb.1  lines  and  arcs, 
which  are  geometrically  and  evenly  joined,  as  shown  in  fig.  5. 
The  necessary  operations  are  fully  indicated  on  the  drawing  itself. 
Theso  operations  are,  for  tho  most  part,  but  the  repetition  and 
combination  of  the  problems  treated  of  in  the  first  division  of  tho 
subject.  We  have,  moreover,  given  somo  of  tho  problems  do 
tached,  and  on  a  larger  scale,  in  figs.  6,  7,  8.  Fig.  (J  recalls  tho 
problem  (35),  which  has  for  its  object  tho  drawing  of  an  arc,  ij  k. 
tangent  to  the  straight  lines,/"'  and  gh,  the  radius,  ok,  being 
given,  equal  to  31-5"'/„.  (fig.  2,  Plate  III.)  This  problem  meets 
with  an  application  at  fgh,  fig.  5.  In  fig.  7  we  have  the  problem 
(37),  which  requires  that  an  arc,  Imn,  be  drawn  tangent  to  a 
straight  line,  nip,  and  to  a  given  arc,  q  r  t,  the  point  of  contact,  n, 
being  known  (fig.  6,  Plate  III.)  This  meets  with  its  application  at 
I  m  n,  fig.  5. 

The  problem  illustrated  by  fig.  8  is,  to  draw  a  tangent,  g'f, 
to  two  given  circles  of  radii,  st  and  o1  A\  respectively.  In 
this  problem  (9),  we  require  to  find  a  common  point,  u,  on  tho 
line,  os,  which  joins  the  centres  of  the  two  circles.  To  effect 
tins,  we  draw  through  the  centres,  o  and  s,  any  two  diameters,  vx 
and  v'  x',  parallel  to  each  other.  Join  two  opposite  extremi 
each,  as  v  and  x',  by  the  straight  line,  ii',  which  will  cut  the  line, 
d  s,  in  the  point,  u.  The  problem  then  reduces  itself  to  the  draw- 
ing of  a  tangent  to  any  single  circumference  (fig.  1,  Plate  I.),  from 
a  given  point,  u.  The  tangents  obtained,  in  the  present  instance, 
will  lie  in  one  straight  line,  and  be  the  line  required — tangent  to 
both  circles.  The  application  of  this  problem  is  at  x  k' I  in 
fig.  4. 

On  fig.  9  we  have  also  indicated  the  solution  of  a  problem  (41), 
which  is — to  draw  an  arc,  y  z,  of  a  given  radius,  a  b',  tangent  to 
two  other  arcs,  having  the  radii,  e' d'  and  e'f*  (fig.  8,  Plate  111.) 
This  problem  is  called  for  in  drawing  the  outliue  of  the  jaw  of  the 
chair,  where  it  runs  into  the  base,  A,  near  the  edge  of  the  bolt- 
hole,  a,  fig.  3. 

To  complete  the  outline  of  the  chair,  it  remains  for  us  to  show 
how  to  determine  the  lines,  g'  h',  which  represent  the  inter 
of  portions  of  cylindrical  surfaces,  as  will  be  gathered  from  tigs.  1 
to  4.  To  avoid  a  confusion  of  lines,  we  have  reproduced  this 
portion  in  figs.  10,  11,  and  12,  which  represent — the  two  former, 
vertical  sections  of  each  cylindrical  portion,  and  the  latter,  the  line 
of  intersection  in  plan. 

We  must  first  determine  on  fig.  12,  wliich  corresponds  to  fig.  2, 
the  horizontal  projection,  i,  of  any  point,  as  i,  taken  on  the  arc, 
g'  V,  in  fig.  10 ;  letting  fall  from  this  point,  on  the  base  line,  L  T,  a 
perpendicular,  i  i,  and  also  drawing  from  it  a  horizontal  line,  i  i*. 
Tins  latter  line  meets  the  cylindrical  outline,  g  k',  fig.  11,  in  i'. 
Project  t3  in  i'  on  the  baso  line,  transferring  it  to  a  line  at  right 
angles  to  the  base  line,  by  means  of  a  quadrant  of  a  circle,  and 
draw  through  tho  point  thus  obtained  a  line  parallel  to  the  base 
line,  and  meeting  the  line  ii  in  ?,  which  will  be  a  point  in  the 
curve  required ;  other  points,  as  /',  n',  are  found  in  a  similar 
manner. 

It  must  be  observed,  that  when  the  two  cylindrical  portions  are 
of  equal  diameters,  their  intersection  with  each  other,  g'hf,  as  will 
be  demonstrated  hereafter,  is  projected  horizontally  :is  a  straight 
line;  the  greater  the  difference  between  the  two  cylinders,  the  more 


> -I  the  line  of  their  intersection  be,  a*  U  apparent  in  fig*. 

The  outlines  of  the  feathers,  r  and  c',  glide  into  th..' 
base,  a  whirh,  in  the   plan,  i-  lha  are, 

tlic  preceding  figures, 

i.ere  remark,  r 

may  br  ii  many  of  the  problem  already  discussed, 

and  also  with  ■ 

the  draughtsman  in  the 
.   actiee.     In  such  olijecta  as  tl 

ud  the 
■rs  with  eaffip 

I  in  their  chair-  irly,  but 

an>  in.-'  each    other,  in   such  a  MfJ 

rtical,  <ri*:  this. 
.!  the  carriages 
may  have  to  run  off  the  rails,  as  is  the  case  more  particularly  in 
runes,  from  the  effort  made  by  tin-  wheel*  to  run  in  :i   - 

r  than  tho  < 
for  the  lik 


RULES   AND   PRACTICAL   DATA 

■     MATERIALS. 

The  various  materials  employed  in  mechanical  m 

-  -tli  with 

injured, 

tkm  of  force  or  mo  to  which  tiny 

•  are  termed,  — ""Ung  to  tin-  mode  in  which  they 
' 

I   Ir.iin  often   rt> 
Brj  calculating 
tensioD*  of  uj  •■  to  the 

•i  and  degree  ol 

BUtSTASCE   TO  COJlntE*- 
153.  Compression  is  a  for.  •  ,-!i.  or  n  inl.r 

Gbre*  or  molecule*  of  any  suh-tam-c  which  is  sub- 
:  ••>  iu  action. 

■its,  a  prism  of  oak,  of  such 
dimensions  thai 

'  •!  by  a 
-tiinclre 
of  transverse  m  -hi  of  from  5. 1  |  square 

f  (ransveme  section. 
■  era],  with  oak  of  cast-iron,  I' 

•  irea,  as  soon  as  the  !• 

nt,  the  resistance  to  compression  m 


-  to  be  eompreaeed  u  f  4,900 

•  >r  of  nearly  "K 
•  crushing,  as  so.. n  as  the 
of  the  |*. ve  aneada  three  time*  the  least  dimension  of  the  traas- 

W*  may  safely  load  bodies  of  various  substance*. 

Table  tf  the  Wmgktl  which  Solid* — such  as  C.iumns,  Ptiastert, 
S       -<rts — iciU  sustain  tcilnout  bring  crushed. 

WOOD*    AM>    URALS. 


Drornntios 

MsMtBsL 


Sound  oak,  . . 
oak,. 

i 


PrepottMa  of  Uaftb  to  Uost  Jim*u 


Up  to  It.        Abo».   II        Abmo  14       Ab....  *l 


TM! 


. 


SToS'ES,    BUCKS,    AM>    VIoETABS. 


Deornptios  of  Ma 


•  M 

Granite  t  V96 

gSJ 

S25 



in 

Marl.le,  hard,  .'. 

whiU 

Freestone,  hanl, 



m  Chatillon,  near  Paris 

U  1'aris, 

185 

S&fi 

from  ■ 

711 

*  trdinar)  ■  427 

■ 

171 

An  i 1 1 )"■  

1 1,1 

or 

bard  and  ».ll  baked 

1 

., .  .  i 

•  I  with  lime  •rater 

Mortar,  1  ■  Id 

"  "         of  lime  and  sand,  . . . 

■         B 


/.'        —To  Bad,  bj  means  of  thi-  • 

•  may  ba  I 

Multiply  the  transient  sectional  itrra  of  the  pitta  r>v  the  n< 


I 

i 


BOOK   OF   INDUSTRIAL   DESIGN. 


the  table  corresponding  to  the  material.,  and  to  the  proportionate 
lengtli  of  the  piece.  And  inversely,  from  the  weight  which  a  piece 
is  to  support,  its  smallest  transverse  section  may  be  determined. 
By  dividing  this  weight,  expressed  in  pounds,  by  the  number  in  the 
table  corresponding  to  the  material,  and  to  the  proportionate  length. 

First  Example. — What  weight  can  be  put  with  safety  upon  a 
pillar  constructed  of  ordinary  bricks,  the  pillar  being  of  a  rectan- 
gular section,  of  50  inches  by  60,  and  the  height  being  below  12 
times  the  length  of  this  cross  section  ? 

We  have  50  x  60  =  3000  square  inches  of  transverse  sectional 
area.     Then,  according  to  the  table,  we  have — ■ 
3000  X  57  =  171,000  lbs. 

Second  Example. — What  must  be  the  transverse  sectional  area 
of  a  square  post  of  sound  oak,  19  feet  8  inches  in  height,  and 
which  will  safely  bear  a  load  of  60,000  lbs.  ? 

According  to  the  table,  if  we  suppose  the  length  to  be  not  more 
than  12  times  the  least  cross  section,  the  number  or  coefficient  of 
compression,  in  pounds  per  square  inch,  is  426'75. 


Then, 
and 


60,000  .    , 

;_„„.  =  140  square  inches; 
42b'  to 


Vl40  =  11-8  inches,  the  length  of  tho  supposed  side. 
Comparing  tliis  11-8  inches  with  the  given  height,  we  find  that 


19  ft,  8  in. 
11-8  in. 


236 
11-8 


=  20. 


This  shows — and  we  have  constructed  the  example  with  this 

view — that  in  this  instance  the  proportionate  length  has  not  been 

correctly  estimated ;  and  therefore,  instead  of  taking  the  number 

426-75,  as  in  the  first  column,  we  must  take  that  in  the  second 

column,  for  a  proportionate  length  of  between  12  and  24  times  the 

cross   section.     The   calculation   will,   consequently,   have   to  be 

rectified  thus — 

60.000  .    , 

=  168-7  square  inches, 

and  VT6S-7   =   13  inches  nearly,  the  proper  dimension  for  the 
cross  section  of  the  post. 

Third  Example. — What  is  the  greatest  load  that  can  be  borne 
with  safety  by  a  solid  cast-iron  column,  3  inches  in  diameter,  and 
12  feet  in  height? 

It  is,  in  the  first  place,  evident  that  the  ratio  of  tho  diameter  to 
the  height  is  12  feet,  or  144  inches,  -5-  3  inches  =  48. 

Consequently, 
the  section  -785  x  32  x  4741-666  =  33,500  lbs. 

In  shops  and  warehouses,  builders  employ  solid  cast-iron 
columns,  instead  of  brick  pillars,  so  as  to  take  up  less  space.  These 
columns  are  generally  calculated  to  support  loads  of  above 
33,000  lbs.  each.  They  are  usually  about  3  inches  in  diameter, 
and  12  feet  high.  In  which  case,  supposing  a  cubic  foot  of  cast- 
iron  weighs  452  lbs.,  they  will  weigh  (3  inches  being  equal  to  -25 
foot)— 

•785  x  -252  x  12  x  452  =  266  lbs. 

If,  instead  of  these  columns  being  massive  or  solid,  we  employ, 
m  place  of  two  of  them,  a  hollow  one,  to  support  the  proportionate 
load  of  66,000  lbs.,  and  being  6  inches  in  diameter,  this  increase 


in  tho  diameter  makes  tho  ratio  of  the  length  to  it  24,  instead  of 
48 ;  and  the  coefficient  to  be  taken  from  tho  table  will  conse- 
quently be  14,225,  instead  of  4742. 

Now,  66,000  -H  14,225  =  4-64  square  inches,  would  be  tho 
cross  section  of  a  solid  pillar,  equivalent  to  that  of  which  tho 
thickness  is  sought.  Since,  however,  the  diameter  of  the  tatter  is 
6  inches,  its  section  of  solidity  would  be — 

•785  x  62  =  28-26  square  inches. 
Then,  deducting  from   this   area   4-64  square   inches,  as  above 
determined,  we  have  28-26  —  4-64  =  23-62,  for  the  cross  sectional 
area  of  the  central  hollow.     From  tliis  we  deduce   the  internal 
diametor,  thus — 

/23-62 


J 


7S0 


=  5'485  inches. 


And,  finally,  the  thickness  of  the  column  will  bo — 

6~5"485  =  -2575  inches. 
2 

The  weight  of  such  a  column,  if  12  feet  in  height,  will  be — 

4-64 

— —  X  12  X  452  =  174-77  lbs. 
144 

This  result  shows  very  markedly  how  great  an  economy  results 
from  the  employment  of  hollow  in  place  of  solid  cast-in. n  columns. 
The  thickness,  determined  as  above,  of  -2575  inch,  is  theoretically 
sufficient,  but  in  practice  we  seldom  find  such  castings  under  half 
an  inch  thick. 

In  the  above  examples,  too,  the  mouldings  usually  added  to  the 
columns  are  not  taken  into  the  account,  With  these,  the  weight 
will  bo  a  tenth  or  so  more,  according  to  the  description  of  moulding. 

TENSIONAL    RESISTANCE. 

155.  A  tensile  force  is  one  which  acts  on  a  body  in  the  direc- 
tion of  its  length,  tending  to  increase  the  length,  and  when  carried 
to  a  sufficient  extent,  to  cause  rupture. 

As  with  reference  to  compression,  many  experiments  have  been 
made  to  determine  the  sectional  area  to  be  given  to  bodies  i  f 
various  materials  submitted  to  a  tensile  strain,  so  that  they  may 
safely  resist  a  given  force. 

First  Example. — Required  the  sectional  area  for  four  square 
tension  rods  of  wrought-iron,  to  connect  the  top  and  bottom  of  a 
hydraulic  press,  in  which  tho  force  which  tends  to  separate  these 
two  ends,  and  consequently  to  rupture  the  rods,  is  equal  to  500,000 
lbs. 

Each  rod  must  be  capable  of  resisting 

500.000  , ., 

=  125,000  lbs. 

4 

According  to  the  table,  the  best  wrought-iron  may  be  safely 

subjected  to  a  strain  of  14,225  lbs.  per  square  inch  of  cross  section. 

We  have,  consequently, 

125.000       0_„  .    , 

=  8-79  square  mches. 

14,225  H 

for  tho  area  of  the  cross  section ;  and 

V879  =  2-964,  or  nearly  3  inches, 

for  a  side  of  the  square  rod.   If  the  rod  were  round,  we  should  have — 


/8-79 
D=V:785  = 


3-345  inches,  for  the  diameter. 


la  the  aamc  maanar,  the  rfkraet  cr  proper  for  air—  engine 
pi»t •  >o -r odi  mar  be  ralmlalod,  when  the  preaaure  on  the  puton  ia 
known. 

'  J  sustain  u-hrn 

submitted  ■  S    11/1. 


DMcnpfca  U  V.u,  ^ 


• 






'  _r»in 





M  

Mi- 

I 

. 
oar  u  i 

'  

j  to  tin-. 



M3*/. 






I  to  -1S  inch, 
k  or  1  !<•  :.  •/■  in  dial 








I 

. 


... 





i 


11 

1  1 

7.1  IS 


417 

l.llrt 

In. I 


440 

826 


110 


v  /  .  d  the  amount  of  lenale  or  I 

,  a  carriage  draw-ahad,  inada 
I  ruaa-aeclional  area  of  166  etjuara  inehea. 

hatt — 
:  Iba.  x  15  5  =  36-400  Iba, 
155.  Pulby  B  ila  mar  gene- 

rally be  employed  in  practice,  to  determine  the  dui 
.»: — 

20_x  II  I' 
• 
in  «rU  h  I  'i  "f  8m  land  in  boaM;  11  P,  the  : 

«rer;  and  r,  tl,-  mute. 

•ii  Iba.,  raiiied 
I  font  Ufljb  in  a  uiinui.  .uumea, 

•>ame  aa 

inula  would  be — 

_  1.V'  •   ■   II  I' 
v 
r,  in  this  ntkoetrai  pel  - 

and  I,  the  width  in  itntiin.:  kaaat  «(  the 

Of  6"/.. 

the  htirse  puirer  by  the  constant  mv.  dnide  the  pro- 
duct by  the  iclucily  in  fret  per  minute.,  and  the  (fuotienl  trill  be  the 
u-idih  <y"  tht  Iximl  in  i 

/                     Let  II F  niinute, 

then, 


10 

- 
j  which  it  embrace*;  tint  b 
ii ;  and  that  ll 

I  !i_\   it. 
It    i- 
of  two  | 

KUM. 

effort  w I 

- 
B  I 

i 

wliilit    Ii 

!  in   the 
-  pported  ut  the  centre,  and  h 
applied  at  both 

u .  der  the  caae  ■ 

.i  ttraln  at  the 
'A    Ih.  iha  ».  i-l, t  la   ; 

in   wU  Ii  tin-   piece   und<  i 
■ 
diuienaion   in  b 
auuilarly  ezprea*ed ; — then  tliv  great.- 


BOOK  OF   INDUSTRIAL   DESIGN. 


bear,  without  undergoing  alteration,  will  be  determinable  by  tho 
following  formula,  the  piece  being  of  rectangular  section,  aud  fixed 
at  one  end,  and  weighted  at  the  other. 

C  X  ab3 


W  = 


6L 


Now, 


C  ==    8,535,  for  wrought-iron  ; 
10,668,  for  cast-iron ; 
854,  for  oak  and  deal. 
Substituting  these  values  of  C,  in  the  preceding  formula,  we 
shall   have,  for  pieces   of  rectangular  section,  according  to   the 
material — 

For  Wrought-iron. 


TbTT 


For  Cast-iron. 


p  ^  10,668 IX«i',  or  more  simp]yi  = 
6  L 


1778  X  ab3 


P  = 


854  x  ab- 
6L 


,  or  more  simply, : 


142  x  ab3 


Tliese  formulae  lead  us  to  the  following  rule  for  pieces  of  rect- 
angular section : — Multiply  the  horizontal  dimension  in  inches  of 
cross  section,  by  the  square  of  the  vertical  dimension  in  inches,  and 
by  a  coefficient  depending  on  the  material:  then  divide  the  product 
by  the  length  in  inches,  and  the  quotient  will  be  the  weight  in  pounds, 
which  the  piece  will  sustain  without  alteration. 

This  rule  is  derived  from  the  fact,  that  the  transverse  resistance 
of  pieces  submitted  to  a  deflective  strain  is  inversely  as  their 
length,  directly  as  their  width,  and  as  the  square  of  their  vertical 
thickness. 

According  to  tliis,  pieces  fixed  at  one  end,  and  intended  to  bear 
a  strain  at  the  other,  should  be  placed  on  edge ;  in  other  worus, 
the  greatest  cross  section  should  be  parallel  to  the  direction  of  the 
strain. 

First  Example. — What  weight  can  be  suspended,  without  causing 
deflection,  to  the  free  end  of  a  wrought-iron  bar,  fixed  horizontally 
into  a  wall  at  one  end,  and  projecting  5  feet  (==  60  inches)  from  it; 
the  bar  being  of  a  rectangular  cross  section,  having  its  horizontal 
dimension,  a  =  1-2  inches,  and  its  vertical  dimension,  b  =  1-6 
inches  ? 

We  have 

1422-5  x  1-2  x  1-63 


P  = 


72-8  lbs. 


This  result  is  obtained  on  the  supposition  that  the  bar  is  placed 
on  edge  ;  but  what  would  be  the  weight,  other  things  being  equal, 
supposing  the  bar  to  be  placed  on  its  side — that  is,  when  1-6  inches 
is  its  horizontal  dimension,  a,  and  1*2  its  vertical  dimension,  bl 

We  have,  in  this  case, 


P  = 


14225  x  1-6  x  1-23 

6U 


=  54-6  lbs. 


This  inferior  result  shows  the  advantage  of  placing  the  bar  on 
edge. 

When  the  piece  under  experiment  is  of  square  instead  of  oblong 
section,  a  necessarily  =  b,  and  a  b-  becomes  b',  and  tins  is  conse- 
quently to  be  substituted  in  the  formual  for  the  former. 


If,  however,  tho  piece   is  cylindrical,  the  formula  will  be — D 

representing  tho  diameter, 

„                .  .  .         _        854  x  D3 
r  or  wrought-iron,  P  =  — — • 


For  cast-iron, 
For  wood, 


P  = 


JL 

1066  x  D3 


P  = 


L 

35  x  D3 
T       ' 

In  each  of  the  cases  just  referred  to,  the  transverse  sectional. 
dimensions  of  pieces  fixed  at  ono  end,  and  submitted  to  a  strain 
at  the  other,  are  determined  by  the  following  formula! : — 


Form  of  Section. 

Rectangular. 

Square. 

Circular. 

Wrought-iron,  .  . 

■— 1& 

63 

PL 
1,422-5 

I)3    = 

PL 

854 

M         PL 

b3 

PL 

1,778 

D3  = 

PL 

1066 

Wood 

■"-£ 

b3 

PL 

142 

D3  = 

PL 

so 

The  rule  derivable  from  these  formula?  for  the  determination  of 
the  transverse  section,  whether  rectangular,  square,  or  circular,  of  a 
bar  or  beam  fixed  by  one  end  and  loaded  at  the  other  is  thus  stated : — ■ 
Multiply  the  weight  in  pounds  by  its  distance  in  indies  from  the  siijt- 
port ;  divide  the  product  by  a  coefficient  varying  with  the  material 
and  form  of  section;  and  extract  the  cube  root,  which  will  give  <" 
inches  the  vertical  dimension,  the  side  of  the  square,  or  the  diameter 
of  the  circle,  according  as  the  bar  or  beam  is  rectangular,  square,  »r 
circular  in  cross  section. 

First  application :  What  should  bo  the  transverse  section  of  a 
rectangular  wrought-iron  bar,  intended  to  cany  at  its  free  end.  and 
at  a  distance  of  5  feet  from  its  support,  a  weight  of  72'8  lbs.,  tno 
bar  being  supposed  to  be  placed  on  edge  ? 

We  have  here, 

72-8  lbs.  x  60  in. 


ab3  — 


1,42 


=3071; 


then,  if  a  be  taken  =  1-2  inches, 

b  =  x  I  "."'*  =  1-6  inches,  the  vertical  dimension. 


/3-071 

V    w": 


Second  application :  'What  should  the  side  of  the  cross  section 
measure,  of  a  square  bar,  under  similar  circumstances  otherwise  ? 


b3  = 


=  3-071,  and 


11225 

3    

b  =  v  3-07-i  =  1-454  in.,  the  thickness  of  the  bar. 
157.  Observations. — When  tho  bar,  or  beam,  under  erperi 
ment  possesses  in  itself  any  weight  capable  of  influencing  its 
resistance ;  or,  besides  the  weight  suspended  or  acting  at  one  end, 
has  a  weight  equally  distributed  throughout  its  length ;  the  trans- 
verse-sectional dimensions  are,  in  the  first  place,  determined  with- 


4 


M  \\S 


art  taking  the  additional  weight  into    consider., 
fee*.  calculated  app  :..iimaie!y.  and  the  half   of    it    added  to  the 
suspended  l««d,  a  fn«h  calculation  being  made  with  this  stun  a* 
a  Ua.i. 

A  bar,  or  beam,  fixed  by  one  end,  and  loaded  at  the  other,  ha* 
always  a  tendency  to  break  off  at  the  ahoi. 

-   ;.j«.rt.  becatue  it  is  on  that  point  th .:  thi 
rfr  atrain  acta  with  the  greatest  leverage.     V. 

the  piece  has  been  determined,  in  a.-. 
with    the   formula)    gh  u\ch    are    calculated    I 

dimension*  of  the  piece  at  the  shoulder;  the  section  may  bt 
firiauy  diminished  towards  the  free  i 

ing  the  material,  and  leasenin.-  I      The 

curve  y  the  parabola,  as  described  in 

i    and  XII.     It  may  also  be  obtained  in  the 
following  man:  ticular  case  nnder  consideration: — 

Calculate  the  t- 

piece,  the  other  data  remaining  as  1-  1  curve 

■ne  which  pa*-  i,  when 

they  are  |4accd  at  distano  •»  from  the  load  equal  t"  : 

'ivy  are  calculated.     This   curve    is   also  given    to   bars, 
beams,  or  shafts,  filed  at  both  ends  and  loaded  in  their  mi 
throughout  their  length.     T 
1 '  .  ■  •    \  1 1 
of  thi*.     S  •   beams  and  side  levers  are  a'  - 

-   shaDS)  as    it    gives    them    a    uniform    r- 


'.    it.  so  that  they  are  not  liable  to  break  or  give  way  in 
any  on.  -  .'.an  another. 

A  bar,  or  beam,  supi~.rt.-d  in  the  centre,  and  loaded  at  either 

support  double  the  weight  ca|*ble  of  being  carried  by 

-imilar  dimensions,  supported  at  one,  and  loaded  at  the 

■I;  it  is,  ind..-d.  e\ident  llial  each  weight  will  only  act 

with  half  the  leverage,  being  only  half  the  **i*'*irr*>  from  the  point 

-•rt. 

..-ly,  a  bar,  or  beam,  '  ••  mitiea, 

and  loaded  in  the  MB)  lible  that  sus- 

.,.  amine  dimensions  fixed  at  one,  and  loaded 
at   tlie   other  end.     Therefore,  in  calculate 

theae  two  last-mentioned  rases,  it  is  necessary  simply  to  dooble 
.  for  the  first  case. 
A  bar,  or  beam,  firmly  and  solidly  fixed  by  both  ends,  »ill  sap. 
port  a  load   four  times  as  great  aa  one  of  the  same  <tinft«M»i»« 
1.  and  loaded  at  the 

|  ...druple  the  above  coefficient  in  thia 
MM, 

iials,  of 
shafts  for  hydraulf 
tain    gn  at    weights,   the    following    j articular   formula    may    be 
■  1: — 

D=  I 
-ses  the  diameter  in  inches,  and  \Y 
be  sustained  in  pounds. 


TABLE   Ol 

THE    DIAXETERS  OF 

.VIM   OF    WATER-WHEEL    AID   OTHER 

sHxrrs  ro«  heavt 

WORK. 

Diuuttl  of  Journal  in  Inch**. 

Diaawur  *f  Josraal  is  tars— 

Tout  basis 

vl  is 

■    ..... 

OaaVtan, 

Wroufht-Irwa. 

Osavbaa. 

WiMfkt-Ina.     . 

; 

•4315 

8 

l 

1 

8. 

i} 

:< 

1099-0 

a 

9» 

2J 

10 

3 

10, 

3} 

11 

i 

IM 

4 

19 

mi 

6 

1      ' 

6. 

13 

'. 

61780 

11  ' 

:  so-0 

61 

11 

730 

7 

Hi 

1.(5 

- 1 

...35 

15 

inula,  the  dial] 
or  journal,  i«   ! 
strain,  in  pounds,  and  multiplying  it  by  the  constant,   i 

:  indli  «,  <t  Joan 

froa  tliat  for 

mula. 

'  Of   what    dial:  spindle  of   a 


Mfl  l«'.  the   t"tal  strain  b> ■'.:  10  lbs,! 

a  ^___ 
D=  ♦'70,000  X  193*  nearly. 

f   (7-987  X  -863  =)  6  9  inches,  will 

j-oee. 

RESISTAXiE    TO   TO    - 

tially  to  any  solid,  tending  to  turn  iu  opposite  ends  in  different 


BOOK   OF   INDUSTRIAL   DESIGN. 


47 


directions,  or  to  twist  it,  it  is  said  to  be  subjected  to  torsion,  and 
offers  moro  or  loss  resistance  to  tins  action  according  to  its  form 
and  composition.  Taking,  for  example,  the  main  shaft  of  a  steam- 
engine,  at  one  end  of  which  the  power  acts  through  a  crank,  set 
at  right  angles  to  it,  and  at  the  other  the  load,  by  means  of  wheel 
gear — the  resistance  which  tins  load  presents,  on  the  one  hand, 
and  on  the  other,  the  power  applied  to  the  crank,  represent  two 
forces  which  tend  to  twist  the  shaft,  subjecting  it  to  the  action  of 
torsion. 

In  machinery,  all  shafts  and  spindles  whieh  communicate  power 
by  a  rotatory,  or  partially  rotatory,  movement  on  their  axes,  are 
subject  to  a  torsional  strain.  Those  which  sustain  the  greatest 
torsional  efforts  are  those  shafts  denominated  first  movers,  the 
first  recipients  of  the  power.  Such  are  the  fly-wheel  shafts  of 
land  engines,  and  (he  paddle-shafts  of  marine  engines.  In  these 
the  action  is  further  complicated  and  heightened  by  the  irregularity 
witli  which,  in  reciprocating  engines,  the  power  is  communicated 
to  them.  Such  shafts  as  carry  very  heavy  toothed  gearing,  but 
receive  and  transmit  the  powor  in  an  equable  manner,  and  without 
a  fly-wheel,  are  termed  second  movers ;  and  finally,  such  as  carry 
only  pulleys,  or  comparatively  small  toothed  wheels,  are  comprised 
in  the  class  of  third  movers.  Such  shafts,  again,  as  meet  with  an 
intermittent  resistance,  as  is  the  case  with  all  cam  movements, 
require  increased  strength  to  meet  this  irregularity  of  action. 

In  constructing  formulae  for  the  determination  of  the  diameters 
of  shafts,  regard  must  always  be  had  to  the  class  to  which  they 
belong,  and  also  to  the  description  of  work  they  have  to  perform. 

As  the  journals  are  the  parts  of  a  shaft  on  which  the  greatest 
strain  is  concentrated,  it  is  obviously  to  the  determination  of  their 
dimensions  that  our  investigation  should  be  directed.  The  prac- 
tical formula,  for  ascertaining  the  diameter  proper  for  the  journal 
of  a  cast-iron  first-mover  shaft,  is — 


x  419. 


Here,  d  =  diameter  of  journal  in  inches. 

H  P  =  the  horse  power  transmitted  by  the  shaft. 

R  =  the  number  of  revolutions  of  the  shaft  per  minute. 

This  formula  is  expressed  in  the  following  rule. 

159.  To  determine  the  diameter  at  the  journals  of  a  cast-iron 
first-mover  shaft : — Divide  the  horse  power  of  the  engine  by  the 
number  of  revolutions  of  the  shaft  per  minute,  multiply  the  quotient 
by  the  constant,  419,  and  extract  (lie  cubic  root,  which  will  be  the 
diameter  required  in  inches. 

For  the  journals  of  cast-iron  shafts  whieh  are  second  movers, 
the  formula  is — 


a/HP 
V-R- 


X206; 


and  for  third  movers- 


3  /iTp 


106. 


These  are,  in  fact,  similar  to  the  formula  given  for  first  movers, 
with  the  exception,  that  for  these  the  constant  multiplier  is  41-9, 
whilst,  for  the  latter  it  is  206  and  106,  respectively. 

160.  For  the  journals  of  wrought-iron  shafts  the  same  formula: 
are  employed,  the  multipliers  only  being  changed;  these  are  249  for 
first  movers,  134  for  second  movers,  and  676  for  tlurd  movers. 


If,  with  a  view  of  suppressing  the  radical  sign  in  (lie  above  for- 
mula, we  raise  both  sides  of  the  equation  to  their  third  or  cubic 
power,  and  further  express  the  multiplier  by  m,  we  have 

d3=  — -  Xm;  ) 

from  which  formula  it  will  be  seen,  that  the  cube  of  the  diameter 
of  the  journal  is  proportional  to  the  force  transmitted.  Similarly, 
the  resistance  of  a  journal  is  proportional  to  tho  cube  of  its  dia-" 
meter.  In  other  words,  one  journal,  of  which  the  diameter  is 
double  that  of  another,  is  capable  of  sustaining  a  strain  eight  times 
greater,  since  the  cube  of  2  is  8. 

161.  As,  in  consequenco  of  tho  necessity  of  extracting  cubic 
roots,  the  calculation,  according  to  these  formula?,  becomes  very 
tedious  and  complex,  wo  have  rendered  it  much  simpler  by 
means  of  the  table  on  the  next  page. 

We  may,  however,  first  observe,  that  the  formula, 

J3       HP^ 
a J  =  -rf-  X  m, 

may  be  put  in  the  form — 

(P_HP 
m         R  ' 
or  again,  reversing  the  terms, 

m  R 

T3  ~  HP' 
If  now  we  divide  the  coefficient,  m,  by  the  cubes  of  the  series, 
1,  2,  3,  4,  &c.,  representing  the  diameters  of  the  journals  in  inches, 
we  shall  obtain  a  series  of  numbers  corresponding  to 
R 
HP' 
Thus,  if  419  be  successively  divided  by  tho  cubes,  1,  8,  27,  64, 
&c,  the  numbers  in  the  second  column   of   the   tablo    will    bo 
obtained;  and  by  dealing  with  tho  other  multipliers  in  like  manner, 
the  numbers  in  the   3d,  4th,  5th,  6th,  and  7th  columns,  will   be. 
found. 

Rule. — When  the  table  is  used,  the  rule  for  determining  tho 
diameter  of  the  journal  of  a  shaft  is  thus  stated: — 

Divide  the  number  of  revolutions  per  minute  of  the  shaft  by  the 
horse  power,  and  find  the  number  in  the  table  which  is  nearest  to  the 
quotient  thus  obtained,  bearing  in  mind  the  class  and  man  rial,  and 
the  corresponding  number  in  the  first  column  will  be  thediaimUr 
required. 

First  Example. — What  should  be  the  diameter  at  the  journals 
of  a  cast-iron  first-motion  shaft,  for  an  engine  of  20  horse  power, 
the  shaft  in  question  to  make  31  revolutions  per  minute? 
We  have — 

Jl 31 

H  P  ~  20 

It  will  be  observed  that  this  quotient  is  the  nearest  to  tue 
number  1-526  in  the  second  column  of  the  table,  nnd  that  1-526  is 
opposite  to  6i ;  the  diameter,  d,  of  the  shaft  journal  should  con- 
sequently be  6i  inches  in  diameter. 

If  a  shaft  for  the  same  purpose  as  the  above  be  made  of 
wrought-iron,  we  must  look  in  the  fifth  column  lor  the  number  to 
which  1-55  approaches  nearest  It  will  he  observed  that  it  lios 
between  the  numbers  1-992  and  1-497,  respectively  opposite  to  5 
and  51  inches  ;  the  diameter  of  the  journal  should  consequently  Ikj 
between  these — sny  about  5J  inches. 


1-55. 


• 


taile  or  w  a*  etch  rot  matt  jocixal*,  cau-clatcd  with  BirrtExcE  to  toemoxal  - 


:  .   •  ••■ 

falHkrfCMlM  CWfM. 

A»um*U  u  Wrasfkt-tna  »L«ru. 

u£» 

■  -Mm. 

f— ..  ' 

Tk.nl  M«r*t«. 

FuM  Vina 

?**     :..  M  .»-». 

Tklnl 

T 

MM  000 

1568-000 

848-000 

.'00 

.000 

«oo 

I 

•00 

906-000 

•00 

•00 

If 

. 

3 

. 

31  125 

3 

4-963 

1 

3  1J3 

4 

41 

5 

sua 

■848 

II 

•637 

■806 

1153 

•313 

•750 

1 

•601 

7j 

•253 

•325 

8 

■838 

•683 

•335 

173 

•no 

9 

■575 

1  14 

•Ml 

1-1 

■121 

156 

10 

>o, 

- 

•178 

• 

•J  15 

■110 

II 

■314 

155 

II 

135 

•089 

II 

119 

111 

•078 

• 

127 

•068 

. 

13 

049 

111 

•084 

II 

153 

•049 

. 

Hi 

137 

15 

•061 

031 

039 

1 

3 

3 

4 

6 

6 

- 

1  Example, — We  require  to  ascertain  flu  d 
urnala  of  a  ahaft  of  the  second  claan.  Intended  to  trans. 
-*-e,  i~jiia1  to  15  horee  power,  at  the  rate  of  40  rev 

iota. 

R        <"       ._ 
-  =  3-67. 

third  column,  a- 

than,  that  if  the  ahaft  ia  to  b 

I 
wn-d  3j  and  1  ..tiout  half  axi 

two  mali-riala  in  thia  inittanrc. 
I 
tranamit  a  force  equal  to  C  homo  power,  v 

Tiola  in. 
•  ..-•  ■  »r>.  ..t.un.ri  ! 

B  60 

nr    - 


-  MS, 


Dtnnbar,  in  tin-  tliinl  • 

-    :ind  3|, 

inches,**  tin-  number,  - 

journalii  and  i! 

■ 

'-ip>n  journal,    . 

- 

tonal  and  a  ladral  or 

wiih  r.  ■  '   -tr-.iiii  which  hi  the  paail    I 

ahaft*  are  not  of  any  great    Itogffa — 3   to   <i   ' 

I  raaMron  ahafta  of  a). 

greater 
than  tli .'  tiaJa. 


BOOK   OF   INDUSTRIAL   DESIGN. 


FRICTION   OF    SURFACES   IN   CONTACT. 

162.  Friction  is  the  resistance  which  ono  surface  offers  to 
another — moving  or  sliding  on  it.  Friction  may  be  distinguished 
as  sliding  friction,  and  the  friction  of  rotation.  The  former  is  that 
which  arises  from  the  simple  rubbing  of  ono  surface  upon  another; 
the  latter,  from  the  rotation  of  one  surface  upon  another. 

The  friction  caused  by  the  rubbing  of  plane  surfaces  is  inde- 
pendent of  the  extent  of  surface  or  velocity  of  movement ;  it 
depends  essentially  on  the  weight  of  the  body,  or,  more  accurately, 
the  pressure  binding  the  two  surfaces  together.  It  may  therefore 
be  said,  that  the  friction  is  in  proportion  to  the  pressure. 

Similarly,  the  friction  of  a  journal  in  its  bearings  is  independent 
of  the  length  of  these,  but  is  proportional  to  the  diameter  and  to 
the  pressure. 

We  give  tables  for  each  of  these  classes  of  friction,  indicating 
the  ratio  (if  the  friction  to  the  pressure,  and  consisting  of  a  series 
of  coefficients,  whereby  the  pressure  must  be  multiplied  in  order 
to  ascertain  the  amount  of  resistance  due  to  friction. 

Table  of  Ike  Ratios  of  Friction  for  Plane  Surfaces. 


Description  of  Materials 

of  the  Fibres. 

Condition 
of  the  Surfaces. 

Ratio  of  Friction 
to  Pressure. 

At 
Starting. 

In 
Motion. 

r 
! 

Oak  on  oak J 

Parallel. 
Do.        | 

Across. 

Do. 

Endwise 
(on  one  piece). 
Parallel. 
Do. 
Do. 
Do. 
Do. 

Flat  or  on  edge, 
j  Flat. 

Dry. 

Lubricated  with 

dry  soap. 

Dry. 

Wet  with  water. 

{            Bry. 

Do. 

Do. 

Do. 

Do. 

Wet  with  water, 

>             Do. 

|  Oiled  or  greased. 

Dry. 

Do. 

Do. 

■62 
|     -44 
•44 
•71 
■43 
•38 
•53 
•80 
■62 
05 
•62 
•12 
<     -47 
|     -28 
•16 
•19 

•48 
•16 
•34 
■25 
•19 

Ash,  beech,  or  deal  on  oak,  . . 

■38 

Wrought-iron  on  oak, 

■49 

Ftimp  leather  on  cast-iron,. . . 
1  on  cast-iron  pulleys,... 

•27 
•15 

Example. — What  power  is  necessary  to  raise  an  oaken  flood- 
gate weighing  30  lbs.,  and  against  which  a  pressure  is  exerted 
equal  to  700  lbs.  ? 

We  have 

(•71  x  700  =)  497  +  30  =  527  lbs.  at  starting, 
and  (-25  x  700  =)  1  i  5  +  30  =  205  when  in  motion, 

supposing  the  pressure  continues  the  same. 


Table  of  the  Rutins  if  Pridian  for  Journals  in  Beari 


Cast  or  wrought-iron  journals, 
in  oast  orwrought-iroii,  brass, 
or  gun-metal  bearings, 


Cast-iron  in  cast-iron < 

Cast-iron  in  brass  or  gun-metal, 

Cast-iron  in  lignumvita; < 


Wrought-iron  in  brass  or  gun- ' 
metal 


Wrought-iron  in  lignumvita:, .  - 


Lubricated  with  oil 
or  lard, 

Similarly  lubricated 
and  wctwitli  water 

Lubricated  with  or- 
dinary oil,  and  wet 
with  water,   

Greased 

1 1  reased  and  wet,  . . 

(Jnlubrioated 

Lubricated  with  oil  and 
lard 

Lubricated  with  o  pre- 
paration of  lard  and 
plumbago,    

I  I  leased, 

i  ireaaed  and  wet,  ». . . 

Badly  lubricated,  7. . . 

Lubricated  with  oil  and 

lard 

Lubricated  with  ordi- 
nary oil 


Rule. — To  determine  the  frietional  pressure,  f,  acting  on  the 
bearings  of  a  journal,  always  bearing  in  mind  the  weigh!  of  the 
shaft  and  the  gear  carried  by  it,  the  power  transmitted,  as  also  the 
resisting  load:  Multiply  the  product  of  these,  p,  by  the  coejjh 
to  obtain  tlie  amount  of  friction;  next  multiply  this  by  the  constant 
•08,  and  by  the  diameter  d.,  in  inches,  (or  by  -08(/..)  to  obtain  the 
amount  per  revolution  ;  and,  final! y,  multiply  this  by  the  numbi  r  of 
revolutions  in  a  minute,  which  will  give  the  amount  of  power  con- 
sumed  by  friction  during  this  unit  of  time. 

Example. — What  amount  of  power,  A,  is  absorbed  by  the 
friction  of  the  journals  of  a  east-iron  shaft  revolving  in  bearings  ; 
also,  of  cast-iron,  under  the  following  conditions? 

The  diameter  at  the  journals  =  5  inches. 

The  pressure  of  the  shaft  and  gear  =  20,000  lbs. 

The  velocity  =  5  revolutions  per  minute. 

According  to  the  table,  the  coefficient,  c,  is  -075. 

Here  we  have — ■ 

F  =  -08  d  x  c  x  P, 
=  -08  x  5  x  -075  x  20,000  =  3,000  lbs. 


CHAPTER    IV. 
THE   INTERSECTION  AND   DEVELOPMENT  OF   SURFACES,  WITH  APPLICATIONS. 


163.  Nowhere  is  descriptive  geometry  more  useful,  in  its  appli- 
cation to  the  industrial  arts,  than  in  the  determination  of  the  lines 
of  intersection,  or  junction,  of  the  various  solids,  whether  the  in- 
tersection be  that  of  two  similar  solids  with  each  other,  as  a 
cylinder  with  a  cylinder ;  or  of  dissimilar  ones,  as  a  cylinder  with 


a  sphere  or  a  cone.  Willi  the  aid,  however,  of  this  branch  ot 
geometry,  we  can  determine,  in  the  most  exact  manner,  the  pro- 
portions  of  all  the  curves — of  double  as  of  single  curvature — which 
may  bo  produced  by  the  intersections  of  surfaces  of  revolution, 
the  constructive  or  generative  data  of  which  arc  known. 


T1IK    I 


Ana  b  which  aoch  care*  occur  are  execed- 
•agtv   n„a«  r . .  n»  ,    tl, rj    abuuo  I 

.,;„(,  of  the  I 

•    ■ 

ablr  to 

al    and    arvliilectural    coo- 


Tin:    I.N      '  0N8   AND    DEVELOPMENT  OF 

[NDERS   AND  CONEB, 


PLATE  XIV. 


AMD   BOILERS. 


I  .is  said 

■ 

"uitiiiti.m  in  tooc*— ion 

•"•n.  by 

- 

000  and 

1  and  2,  draw 

- 

1  t',  and/1/*. 

and  in  r*  J'  in  the  vertical  pr< 

-  dmWB  in  plan 
-',  it  will 
-  ■  if  the 
throuirh 

intersection  of  thin  Una,  r'  ./.  with  t>. 

r.  A. 

-  m  n,  parallel 

I 
\ 

in',  p.  when,  ait  in  ill!- 
•jmt,  ||n 


A*  n 

■ 

wliich  an  n  a  plane  a! 

other — ;- 

nth. 

-.  and  i:, 

■ 

that  in 

- 

1  5,  which  n 
is  a  species  of  man  ! 

Tin;  n 

'■' 

■ 
ntained  within   • 

ii  will  l»'  tin-  outline  of  that  |«irt  ■•: 
. 

■  ',  by  any  plane  wh.v. 
itting  plane,  a'  f,  for   in»!..  h 

■ 
straight  line,  as  in  fig.  3*.  and  as  a  i 


BOOK   OF   INDUSTRIAL   DESIGN. 


of  projection  to  which  it  is  parallel.  It  follows,  from  the  existence 
of  these  respective  properties,  that  we  have  at  hand  a  very  simple 
nn  thod  for  determining  the  curve  of  intersection  of  a  cone  with  a 
sphere,  whatever  may  be  the  relative  position  of  their  axes.  This 
method  consists  in  supposing  a  series  of  parallel  planes  to  cut 
both  the  cone  and  the  sphere,  so  as  to  produce  circular  sections 
of  both — the  intersections  of  the  oudines  of  which  will  conse- 
quently be  points  in  the  curve  sought,  as  indicated  in  fig.  3. 

The  intersection,  a1  b',  is  a  circle,  the  diameter  of  which  is  limited 
bv  the  extreme  generatrices,  s'  a',  s'  b,  of  the  cone,  where  they 
encounter  the  great  circle  of  the  sphere,  c.  The  same  method 
holds  good'  when  the  cone  is  cut  by  any  plane,  a!  g,  inclined  to  the 
base,  the  outline  of  the  section  being  in  this  case  an  ellipse,  which 
is  projected  in  the  plan,  fig.  3,  by  the  line,  a  i"  g'  n',  the  resultant 
of  the  various  intersections  in  the  planes  adopted  in  die  construc- 
tion and  obtaiument  of  the  curve. 

The  same  occurs  with  the  intersection  of  a  cone,  a'  e'  s',  with  a 
cylinder,  a'b'  if;  and  when  dicir  axes  lie  in  the  same  straight 
line,  the  intersection,  a  b',  is  also  a  circle,  the  ditmeter  of  which 
is  equal  to  that  of  the  cylinder. 

167.  If  their  axes  are  parallel,  though  not  in  the  same  straight 
line,  the  intersection  of  these  two  surfaces  becomes  a  carve  of 
double  curvature,  which  may  be  determined  either  according  to 
the  method  adopted  in  reference  to  figs.  1  and  3,  or  by  supposing 
a  series  of  plains  to  cut  the  cone  parallel  to  it.s  base,  and  conse- 
quently at  right  angles  to  the  generatrix  lines  of  the  cylinder;  by 
this  means  circular  sections  will  be  produced,  those  of  the  cylinder 
being  always  tin  same,  but  those  of  the  cone  varying  according  to 

•  if  the  planes  from  its  apex.  The  points  of  intersec- 
tion of  he  various  circles  representing,  respectively,  sections  of 
the  cone  and  cylinder,  will  be  points  hi  the  curve  of  intersection 

SUil<   lit. 

DEVELOPMENTS. 

168.  By  this  term  is  meant  the  unrolling,  extending,  or  flatten- 
upon  a  plane,  of  any  curved  surface,  in  order  to  ascertain 

its  exact  superficial  measurement. 

i  The  more  generally  used  surfaces  or  forms  which  are  capable 
of  development  in  this  manner,  are — the  cylinder,  the  cone,  prisms, 
pyramids,  and  the  frus/a,  or  fragments  of  these  solids. 

Tin  and  copper-smiths  and  boiler-makers,  who  operate  upon 
metals  which  come  into  their  hands  in  the  form  of  thin  sheets, 
have  continually  to  transform  these  sheets  into  objects  which  are 
analogous  in  form  to  these  solids. 

To  do  their  work  with  skill  and  exactitude,  and  not  by  mere 
guess,  and  also  to  avoid  the  cutting  of  the  material  to  waste,  they 
should  make  plans  of  the  whole  or  part  of  the  object  as  finished, 
so  that  they  may  calculate  the  exact  development  of  the  surface, 
both  as  to  form  and  size,  and  cut  it  at  once  from  the  sheet  of 
metal  with  all  possible  precision. 

THE   DEVELOPMENT    OF    THE    CYLINDER. 

169.  Here,  taking  fig.  2,  which  we  have  on  a  former  < 
considered  as   a   couple   of  solid  cylinders,  to   represent,  in  the 
present  case,  two  pipes  or  hollow  cylinders  formed  of  thin  sheet 
metal,  let  us  set  about  ascertaining  what  should  be  the  shape  and 
size  of  the  pieces  of  metal  as  extended  out  flat,  of  which  these 


two  cylinders  are  to  be  formed.      It  is  to  be   observed,  in  the  first 

place,  that  the  rectification  or  development  into  a  straight  line  of 
a  circle,  is  equal  to  its  diameter  multiplied  by  3-1416.  &c;  whence 

tin-  development  of  the  base,  r  q,  of  the  right  vertical  cylinder,  A. 
fig.  2}  of  which  the  diameter  measures  -322  metres,  is  obviously 
equal  to   3-22  X  31416  =  1012  m. 

This  length,  then,  1-012  m.,  is  set  off  on  the  fine,  M  M.  fig.  10, 
and  the  circumference  having  been  divided  into  a  Dumber  of  equal 
part-,  as  was  done  to  obtain  the  curve  of  intersection  of  the  two 
cylinders  in  fig.  1 ;  the  line,  M  M,  is  divided  into  the  like  number 
of  equal  divisions.  Through  each  of  these  points  of  di 
perpendiculars  are  erected  upon  the  line,  m  H,  representing  so 
many  generatrix  lines  corresponding  to  those  of  the  cylinder,  a, 
fig.  2;  and  for  the  sake  of  greater  intelligibility,  we  have  marked 
the  corresponding  lines  bv  the  same  letters.  Next,  on  each  of 
these  are  set  off  distances,  M  4',  e'  e-,  I'  I2,  P  a',ff2,  u'  u-,  q 
equal  to  the  respective  distances  in  fig.  2.  By  this  means  are 
obtained  die  points,  b1,  e,  X,  &e.,  in  fig.  10,  through  which  the  can  e 
passes  which  forms  the  contour  of  intersection  correspi  Hiding  to  that 
portion  of  the  senii-cylhider,  V  a  b",  fig.  1,  which  is  intersected  by 
the  horizontal  cylinder,  b;  and  as  the  other  half  of  the  cylinder  is 
precisely  the  same,  the  curve  has  simply  to  be  repeated,  as  shown 
in  fig.  10. 

It  is  unnecessary  to  detail  the  method  of  finding  this  d 
ment  of  the  horizontal  cylinder,  B,  as  it  is  identical  hi  principle 
to  that  just  discussed. 

It  may  be  gathered  from   the   above    iv:  lhat  the 

principle  generally  to  be  followed  in  i 
cylindrical   surfaces,   is,   first,  to   unfold  it  in    a  di  • 
angles  to  one  of  its  generatrici  i.eratiix 

takes  in  the  construction  of  the  solid,  and  ther  to  set  <  ff  from  the 
straight  line  thus  produced,  at  equal  distances  apart,  any  number 
of  distances  previously  obtained  hum  the  projections  of  ihe  out- 
line or  line  of  intersection  when  the  cylinder  is  joined  to  another, 
or  of  its  section  when  cut  by  any  plane.  The  curve  of  this  out- 
line is  finallv  obtained  by  tracing  a  line  through  the  exti 
of  die  generatrices,  drawn  perpendicular  to  thi 

THE   DEVELOPMENT    OP    THE 
170.  As  in  the  case  of  the  cylinder,  so  likewise,  in  order  t"  find 

the  development  of  tin-  cone,  do  we  unfold  it,  as  it  were,  in  the 

direction  of  motion  of  its  generatrix.     Now,  as  all  the  generatrices 
.   of  a  right  cone  an-  equal,  and  converge   to  one  point,  the  apex,  it 
follows  that,  when   the  conical  surface  is  developed  upon  a  plane, 
these  ge,  U  form  radii  of  a  portion  of  ad 

quently,  if  with  one  of  the  generatrices,  as  a  radius,  we  describe 
a  circle,  and  cut  off  as  much  of  the  circumference  as  shall  be  equal 
to  that  of  the  base  of  the  developed  cone,  we  shall  obtain  a 
sector  of  a  circle  equal  in  area  to  the  lateral  surface  of  the  cone,  BS 
developed  upon  a  plane. 

Fi".  9  represents  the  development  of  the  frustum,  or  truncated 
cone,°  a'  I",  a'  b',  as  projected  in  fig.  3%  and  of  which  the  apex 
would  bo  s',  were  the  cone  entire.  The  operation  is  as  fol- 
lows:— 

We  dial]  suppose  the  cone  to  be  developed  in  the  direction 
taken  by  the  generatrix,  s'  a',  fig.  3';  therefore,  with  a  radius  equal 


>M\VS 


■',  describe  the  fragm)  nl  of  a  circle, 

/'  ■»  Ar. 

■  ireular  !«•.■    I 
•ante  arbitrary  number  of  equal  part*,  aay  1 1  drawn 

•In-  arc, 
a    ■    a1,  fitf.  9.  an  equal  nun. 

t 
!  lraw  the  radii, 

■ 

.ireular 

.  t..  the 

.ire,  a'  b'  a'. 

radius  drawn  with  the  same  I  with  a  radius  equal  to 

away. 
iSlc  •!■ 

an  ani 

171    I  e,  of  which  the  dividing  plana 

- 
Irii;d  or  spherical  body,  and  1 1 >«-  Hue 
ed  in  any  «ny.  the  development  of  tl 

take  the  f"nn  of  the  are,  a  e  6. 
•    .tT.  on 

. 

■ 

■ 

I 

i    "in«t  !»• 

. 

Cor  the 

■■  ncrally 

I 


the  development  of  one  of  euch  goree;  th-  : -awing 

(/,  an  are,  m  n,  corr>  - 

•  • 

.-.  a«  wo  in  tl  i  '    tin-  arc,  m  n, 

fig.  6,  mark  an  arbitrary   III  la,  at   equal  dialancea 

; 

the  varioua  r 
■  kfcfc  arc*  are  drawn  a*  indicated ;  the  ix-etifica- 

I.  and  transferred    to    )>  ■]«  ndiculara 
drawn  th 

Ihe  arc,  m  n.  wj 
Thus,  from  tin-  an-,  ;.  <j.   -  '  </',  and 

siniilarh 

tin-  aurl  The 

necessary  allowance,  for  lap  is  superadded.  a»  shown  bj 

'. 
-    tin  n   hammered    to  a    pr-  , 
an  til,  w  -irface. 


THE  DELINEATION  AND  DEVELOPMENT  OF  ID  I 
BCREWS,  AND  BERPENTLNEa 

P  L  a  T 1    xv. 

id  i 
n:t.  That   emrj    is  called  a  eylii 

■ 

and  in  tl 

■ 
rum  it  -  ' 

time  .-<  ; 

int..   tl  ■ 
drawn   ; 

Let 

point  pn.jivt.il  in  n  >l 

I.  a   m  r- 
I  I 

;.  irta,  ami  a  •' 
drawn  ■  .   theea 


BOOK  OF  INDUSTRIAL  DESIGN. 


S3 


points  are  next  connected  by  the  continuous  line,  a',  1',  3',  6',  9', 
a-,  which  forms  the  vertical  or  lateral  projection  of  the  helix. 

Half  of  this  curve  is  indicated  by  a  sharp  full  line,  as  being  on 
the  front  surface,  a,  3,  6,  of  the  cylinder,  whilst  the  other  half  is 
in  dotted  lines,  representing  the  portion  of  the  curve  which  is  on 
the  other  side,  a,  9,  6. 

The  number  of  divisions  of  the  circumference  of  the  cylinder 
is  a  matter  of  indifference  as  regards  the  accurate  delineation  of 
the  curve,  and  it  is  therefore  natural  to  choose  a  number  that 
calls  for  the  simplest  operations — an  even  number,  for  example, 
as  6,  8,  or  12;  and  in  the  present  instance,  wherein  the  starting 
point,  a,  lies  in  the  horizontal  diameter,  a  6,  of  the  base,  it  will 
be  observed  that  two  points  occur  in  the  same  vertical  line,  as 
2 — 10,  which  gives  the  points,  2',  10',  in  the  vertical  projection. 

The  operations  will  be  similar,  if  the  given  starting  point  be 
diametrically  opposite  to  a,  as  b',  the  pitch,  bl  b2,  being  equal  to 
a1  a2. 

174.  The  conical  helix  is  different  from  the  cylindrical  one, 
simply  in  that  it  is  described  on  the  surface  of  a  cone  instead 
of  on  that  of  a  cylinder,  and  the  operation  consequently  differs 
very  slightly  from  the  one  before  described ;  the  horizontal  and 
vertical  projections  of  the  cone  are  given,  and  also  the  pitch. 
Fig.  3  is  the  vertical  projection  of  a  truncated  cone,  c,  the  bases 
of  which,  a'  b',  c'  d',  are  represented  in  the  plan,  fig.  1,  by  the 
concentric  circles  described,  with  the  respective  radii,  a  o  and  c  o. 
The  outer  circle  having  been  divided  as  already  shown,  radii  are 
drawn  to  the  centre,  o,  from  all  the  points  of  division,  1,  2,  3, 
&c.,  which  cut  the  inner  circle  in  the  points,  e,f,g,  &c.  These 
points  are  then  projected  upon  the  upper  base,  c'  d',  in  fig.  3,  those 
on  the  outer  circle  being  similarly  projected  on  the  lower  base, 
a'  b' ;  the  respective  points  in  each  base  are  next  joined,  thus  forming 
a  series  of  generatrices  of  the  cone,  as  l2 — e2,  22 — /-,  o1 — o2,  &c, 
which  would  all  converge  in  the  apex,  if  the  cone  were  complete. 
These  lines  are  cut  by  horizontals  drawn  through  a  corresponding 
number  of  divisions  in  the  length  of  the  given  pitch,  a'  c',  and  the 
points  of  intersection  thus  obtained  lie  in  the  curve  which  it  is 
required  to  draw.  The  horizontal  projection  of  the  curve  is  then 
obtained  by  letting  fall  from  the  points  of  intersection  last 
obtained,  a  series  of  verticals  which  cut  the  respective  radii  in  the 
plan,  fig.  1.  This  produces  a  species  of  spiral,  or  volute,  e3,/3,  g3, 
A3,  23,  &c.  By  following  out  the  same  principle's,  helices  may  bo 
represented  as  lying  upon  spheres,  or  any  other  surfaces  of  revo- 
lution. 

THE  DEVELOPMENT  OF  THE  HELIX. 

175.  It  will  be  recollected  that  a  cylinder,  and  also  a  cone,  are 
capable  of  being  developed  upon  a  plane  surface,  and  that  the 
h;i-e  of  either,  when  rectified,  or  converted  into  a  straight  line,  is 
equal  to  the  diameter  multiplied  by  3-1416.  Let,  then,  a  6,  fig. 
4,  be  a  portion  of  tho  development  of  the  base  of  the  cylinder, 
A,  figs.  1  and  2;  to  obtain  the  development  of  the  helix  drawn 
upon  ibis  cylinder,  we  must  first  divide  it  oft'  into  lengths,  corre- 
sponding and  equal  to  the  arcs  obtained  by  the  division  of  the 
circle,  a  o.  On  each  of  the  divisions  thus  obtained,  as  1,  2,  3, 
&...  we  then  erect  perpendiculars,  making  them  equal  respectively 
to  the  distances  from  the  starting  point)  (7,  of  the  several  divisions 


of  tho  pitch.  The  extremities  of  these  perpendiculars,  as  1',  2', 
3',  &c,  will  be  found  to  lio  in  the  same  straight  line,  a  G',  which 
consequently  represents  the  development  of  a  portion  of  lire 
helix.  In  general,  the  development  of  a  helix  is  a  straight  line, 
forming  the  hypolhcnuse  of  a  right-angled  triangle,  the  base  .,1' 
which  is  equal  to  the  circumference  of  the  cylinder,  and  the 
height  to  the  pitch  of  the  helix. 

Several  helices  drawn  upon  the  same  cylinder,  and  having  tho 
same  pitch,  or  a  helix  which  makes  several  convolutions  about  a 
cylinder,  is  represented  by  a  series  of  parallel  curves,  the  distance 
between  which,  measured  on  any  lino  parallel  to  the  axis,  is 
always  equal  to  the  pitch. 

The  development  of  the  conical  helix  may  be  obtained  by  means 
of  an  operation  analogous  to  that  employed  for  the  development 
of  the  cone  (Plate  XIV.) ;  and  in  this  case  the  result  will  he  a 
curve,  instead  of  a  straight  line. 

We  meet  with  numerous  applications  of  the  helical  curve  in  the 
arts,  for  all  descriptions  of  screws;  and  staircases,  and  serpentines. 

SCREWS. 

176.  Screws  are  employed  in  machinery,  and  in  mechanical 
combinations,  either  for  seeming  various  pieces  to  each  other,  so 
as  to  produce  contact  pressufe,  or  for  communicating  motion. 
Screws  are  formed  with  triangular,  square,  or  rounded  threads  or 
fillets. 

A  screw  is  said  to  have  a  triangular  thread,  when  it  is  generated 
by  a  triangle,  isosceles  or  not,  the  three  angles  of  which  describe 
helices  about  the  same  given  axis,  situate  in  the  same  plane  as  I  ho 
triangle.  Figs.  5  and  5"  represent  the  projections  of  a  triangular- 
threaded  screw,  such  as  would  be  generated  by  the  helical  move- 
ment of  the  triangle,  a'  b'  c',  of  winch  the  apex,  a',  is  situate  on 
a  cylinder  of  a  radius  equal  to  a  o,  and  of  which  the  other  angles, 
b',  c',  are  both  situate  on  the  internal  cylinder,  Inning  the  radius, 
b  o,  winch  is  called  the  core  of  the  screw,  and  is  concentric  with 
the  first.  The  Wfference,  a  b,  between  the  radii,  a  o  and  b  o,  indi- 
cates the  depth  of  the  thread. 

When,  as  in  the  case  taken  for  illustration,  the  screw  is  single- 
threaded,  the  pitch  is  equal  to  the  distance  between  the  two  points, 

V  and  c';  that  is,  to  the  base  of  the  triangle.     The  screw  is  "i f 

2,  3,  4,  or  5  threads,  according  as  the  pitch  is  equal  to  •!. 
5  times  the  base  of  the  generating  triangle.  From  what  has 
already  been  discussed,  tho  method  of  delineating  the  triangular- 
threaded  screw  will  be  easily  comprehended ;  for  all  that  is  neces- 
sary is  to  draw  the  helices,  generated  by  the  three  angular  points, 
in  the  manner  shown  in  reference  to  figs.  1  and  2.  We  have, 
notwithstanding,  given  the  entire  operation  for  one  semi-convolu- 
tion  of  the  thread,  in  figs.  5  and  5*.  When  one  of  the  exu 
o'  3'  6',  is  obtained,  it  is  repeated  as  many  times  as  there  are  COS 
volutions  of  the  thread  on  the  length  of  the  screw.  To  do  this 
with  facility,  and  without  repeating  the  entire  operation,  it  is 
customary  to  cut  out  a  pattern  of  the  curve  in  hard  card-board, 
or,  by  preference,  in  veneer  wood;  then  setting  this  pattern  i"  the 
points  of  division,  d'  e  f,  previously  set  oil",  the  curves  an 
drawn  parallel  to  one  another.  The  same  may  be  done  with  tho 
inner  helical  Curves. 

It  nius!  I»    observed,  that,  to  complete  the  outline  of  the  screw, 


J  by  :!»■  portion*,  f  -f.  J'  "'■ 
an  drWB  aa  Min}>!< 

■ 

•kin,  a'  I/,  */  •''-•'<•.      Ill  |t 

ided  aerew — Ih 

a'  d\  marks  ti  • 

I 
casual  ' 

r,  in  the 

■ 

:.  in  ail  nuu-s  having  as  in.. 

- 

BWE 

'.tl   out 

cut  away  from  it — in  anch  a  manner  thai  it-  more  i:> 

t 

■   ' 

9  ■ 
Meea*-./  by  a  |>lane  pan 

6*  and  '•' 

I  into  it ; 

■ 
!■.  E;  and  aa  '■■ 

\>\  Uie 

■ 


Thia  form  'u  oftrn  employ .  »  a,  such 

I 

tin-  ml. 

I| 

I 

.    an. I    already 

- 
■ 

Of  ili-tinet  ;   til  u 

in  the  point,  J,  "n  lb 

.  OJ   the 

'n  i  •  ■  i 

■ 
r     i 

■ 

In     tl: 

lerv  « •units  are  - 

..njjular- 
- 
I 
■ 
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atl  I    smaller,   at 

' 

For  tl 

; 
■ 


BOOK  OF  INDUSTRIAL  DESIGN. 


THE    APPLICATION  OF  THE  HELIX. 

THE    CONSTRUCTION    OF    A   STAIRCASE. 

PLATE   XVI. 

181.  The  staircases,  which  afford  a  means  of  communication 
between  the  various  floors  of  houses,  are  constructed  alter  various 
systems,  the  greater  number  of  which  comprise  exemplifications  . 

of  the  helix.  The  cage,  or  space  set  apart  for  the  staircase,  varies 
in  form  with  the  locality.  It  may  be  rectangular,  circular,  or 
elliptic. 

Fii's.  1  and  2  represent  a  staircase,  the  cage  of  which  is  rec- 
tangular; tills  space  being  provided  for  the  construction  of  the 
main  frame  of  the  stair,  with  its  steps  and  balustrade,  and  with  a 
central  space  left  sufficient  for  tho  admission  of  light  from  above. 
Li  the  ease  of  a  cylindrical  cage,  the  curve  with  which  the  steps 
rise  is  helical  from  bottom  to  top ;  but  in  a  staircase  within  a  rec- 
tangular cage,  the  steps  rise  for  some  distance  in  a  straight  line, 
and  only  take  the  helical  twist  at  the  part  forming  the  junction 
between  the  rectilinear  portions  running  up  alternate  sides  of  the 
rectangle.  Stairs  are  sometimes  made  without  this  curved  part, 
a  simple  platform,  or  "  *estiiig-plaec,"  connecting  the  two  side 
portions. 

For  the  division  of  the  steps,  we  take  the  line,  efg  h  i,  passing 
through  tho  centre  of  their  width,  and  taking  exactly  the  direction 
it  is  intended  to  give  the  stairs.  The  first  or  lowest  step,  A, 
which  lies  on  the  ground,  is  generally  of  stone,  and  is  larger  and 
wider  than  the  others. 

For  the  stairs,  as  for  the  helix,  the  pitch  or  height,  say  3-38  m., 
from  the  basement  to  the  floor  above,  is  divided  into  as  many 
equal  ['arts  as  it  is  wished  to  have  steps.  The  centre  line,  efg  h  i, 
is  also  divided  into  a  like  number  of  equal  parts.  In  general,  the 
number  of  steps  should  be  such,  thai  the  height  of  each  does  not 
exceed  19  or  20  centimetres.  The  larger  the  staircase  is,  the 
mure  may  this  height  be  reduced — say,  perhaps,  as  low  as  15  or 
16  centimetres.  The  width,  1 — 2,  of  the  step  should  not  be  under 
18  to  20  centimetres. 

If,  for  example,  in  the  given  height  of  3'38  m.,  we  wish  to  make 
21  steps,  we  must  divide  this  height  into  21  equal  parts,  and  draw 
a  series  of  horizontal  lines  through  the  points  of  division,  which 
will  represent  the  horizontal  surfaces  of  tho  steps. 

For  those  steps  which  lie  parallel  to  each  other,  it  is  simply 
requisite  to  erect  verticals  upon  the  points  of  division  on  the 
centre  line  in  the  plan.  The  points  of  intersection  of  these  with 
the  horizontals  above,  as  1,  2,  3,  4,  fig.  2,  indicate  the  edges  of ihese 
steps.  For  the  turning  steps,  however,  or  winders,  as  those  steps 
are  called  which  are  not  parallel  to  each  other,  a  particular  opera- 
tion is  necessary,  termed  the  balancing  of  the  steps,  the  object  of 
which  is  to  make  the  steps  as  nearly  equal  in  width  as  possible, 
without,  at  the  same  time,  making  them  very  narrow  on  the  inner 
edges,  or  rendering  the  twist  or  curve  too  sharp  or  sudden. 
Where  the  stairs  are  narrow,  as  in  the  case  we  have  illustrated, 
the  balancing  should  commence  a  step  or  two  before  reaching  the 
curved  portions.  This  balancing  may  be  obtained  in  the  follow- 
ing manner: — A  part  of  the  rectilinear  portion,  p  I,  equal  to  three 
stops,  is  developed,  and  then  a  part  of  the  curved  portion,  I  in  n. 


equal  to  three  more  steps.  On  the  vertical,  t  q,  Bg.  3,  set  off  tho 
heights  of  the  first  three  steps;  and  through  the  point,  q,  draw 
the  horizontal,  (/  -1,  representing  the  development  of  the  widths  of 
the  steps  in  a  straight  line.    Also,  on  the  prolongation,  /  q1,  of  the 

vertical,  t  q,  set  off  the  heights  of  other  three  steps.  Through  the 
point,  <;',  draw  a  horizontal,  and  make  </  10  equal  to  the  are,  /  in  n, 
in  the  plan,  fig.  1,  as  rectified.  The  straight  line,/  10,  will  then 
be  the  development  corresponding  to  the  curve  of  the  framepiece. 
At  the  latter  point,  ?i,  erect  a  perpendicular  on  this  line,  and  at  the 
point,  5,  a  perpendicular  to  the  straight  line,/  4.  The  point  of 
intersection,  o,  of  these  two  perpendiculars,  gives  the  centre  of 
the  arc, p  h  n,  which  is  drawn  tangentiaUy  to  these  lines.  Then, 
through  each  point  of  division  on  the  vertical,  q  q>,  draw  horizon- 
tals,  meeting  this  curve  in  the  points,  j,  k,  I,  in,  through  which 
draw  parallels  to  q  q'.  Then  transfer  the  respective  distance,. 
j  6,  k  t,  I  8,  m  9,  comprised  between  the  arc  and  the  two  straight 
lines,  (  4  and  /  u,  on  the  line  of  the  framepiece,  /;  /.•  n,  in  the  plan, 
fig.  1,  as  at_;  k,  k  I,  I  m,  m  n.  Next,  draw  straight  lines  through 
the  points,/,  k,  I,  m,  and  through  the  respective  points  of  division, 
6,  7,  8,  9,  on  tho  centre  line,  which  will  give  the  proper  incli- 
nation for  the  steps  as  balanced.  The  second  half  of  the  curvutl 
portion  is  obviously  precisely  the  same  as  the  first  in  plan,  and 
may  easily  be  copied  from  it. 

Having  thus  determined  the  position  of  the  steps  in  the  hori- 
zontal projection,  they  must  next  be  projected  on  the  vertical 
plane,  by  means  of  a  series  of  verticals,  which  cut  the  respective 
horizontals  drawn  through  the  points  of  division,  1,  2,  3,  1.  As 
in  tig.  2,  the  anterior  wall  of  the  cage  is  supposed  io  be  CUl  a«  J 
by  the  line,  a  6'  10',  in  the  plan,  the  outer  edges  of  the  steps  are 
seen  and  are  determined  by  erecting  verticals  on  the  correspond 
ing  points,  6',  7',  8',  9',  &c. 

The  perpendicular  portions,  v  i',  of  the  steps,  which  are  over- 
hung by  the  horizontal  portions,  and  consequently  invisible  in  the 
plan,  tig.  1,  are,  nevertheless  indicated  there  in  dotted  lines, 
parallel  to  the  edges  of  the  steps.  To  render  them  quite  distinct, 
however,  and  at  the  same  time  to  show  the  manner  in  which  they 
are  fitted  into  the  framepiece,  we  have  represented  them,  in  ti u-  I, 
without  the  actual  steps,  supposing  them  to  be  cut  in  succession, 
horizontally,  through  their  middles. 

The  framepiece  is  the  principal  piece  in  the  staircase.  It  is 
situated  in  the  centre  of  the  cage,  and  sustains  each  step,  and, 
consequently,  must  he  constructed  \ciy  accurately,  lor  upou  it,  in 
a  great  measure,  depends  the  strength  and  solidity  of  the  stairca>e. 
For  a  staircase  of  proportions,  like  those  of  the  one  represented  in 
the  plate,  the  framepiece  is  generally  made  of  oak,  in  three  pieces  ; 
the  middle  piece,  c,  corresponding  to  the  curved  portion,  whilst 
the  other  two,  B  and  D,  joined  to  that  one,  form  the  rectilinear 
portions.  A  special  set  of  diagrams  is  necessary,  to  determine 
the  shape  and  proportions  of  the  various  parts  of  this  framepiece. 
The  method  here  to  be  followed  is  in  the  first  place,  to  draw  the 
joints,  by  Which  the  vertical  portions  of  the  steps  are  attached  Io 
the  framepiece,  These  can  easily  be  obtained  by  squaring  them 
over  from  fig.  4' to  fig.  5,  in  which  last  are  the  horizontal  division 

lines,  corresponding  to  fig.  2.    It  will  I bserved,  that  th 

referred  to  are  beville.l  oil',  so  as  not  to  l«-  apparent  externally, 
The  faces  on  the  framepiece  are  seen   on  tig.  5.  at  the  parts,  B,  c, 


and  the  method  of  obtaining  them  U  nufT  . 

The  i'taii.t  i-i-v.-  ha*  a  certain  rrjjuUr  i 

■ 

-  <i'  It  and  «*/■,  are  naturally  pa 

•.  d'  <•', 

■l-  r3.      If,   ill    • 
■      the  r 

IS,  ami    14,  1 

■ 

rallelopipad,  in  which  ; 

a  the  junction  of  iliis 
;  -.  ■  and  d,  they  an-  connected  bj  ir. 

or  bin. I  In,  or  by  bulla   pausing  through,  th 

tnickneai  of  the.  wood. 

in  plan  ami  elevation,  the  di  I 
tlio  Ian  .  •  of  the 

■taire,  ;.  ,1   with   th.-   upper  floor.     It   ba   «illi  thin 

lI  the  upper  portion,  d,  of  tin 

the  other  port 

through  the  line,  1 — 'J, 

B  —  <;.    Tin-  form,  dim 
all  fully  imli.-ii^l  ii. 
I 

ipied  by  ■  balustrade,  formed  by  ■ 
of  iron  or  wood,  attached  at  their  lower  exti 

16,  an.)  united  abort  by  a  Mat 
bar  of  U  I  of  poliahed  fumjtnn 

1  .  ii;'.  0.    The  position  of  the  r.«l-, 
I 
• 


Till;    INTERSECTION    OF    81  ELFACER 

41  I 

i-i.vn:  xvii. 

- 

m  pro- 
-.My  met.  with, 

•i  Iflnetmtkm. 

of  which 

•    BM   .•..!Miiiii:ii.-:ii;  .11  Hipm-fl 

I  A,..||- 


■ 
■i.     Tin- 

|«rt  of  : 

- 

\ 
III  tin 

the  key,  ilu-  i 

. 
handle,  r,by  meena  of  which  it  i»  turned. 

i.'i  tin-  r.H-k  by  a  nut.  '•.  work 

projecting  end  of  thi 
cock,  end  fig. 

i 
through  the  Bne,  1  —  3 
ction  through  the  llni 
It  wfll 
• 

to  And,  ■  ■  •..  the  projeeti  i  of  the, 

elliptic  shoulder,  i>,  with  the  external 

■  of  tin-  cylind 
.-  well  when  th 

tlti—  pfau  '.'.  .;,„.  i|„, 

i  with  tin-  i 

. 
section  oi  ■  prism  with  ■  iph  of  the 

ill.-  koy  in  il 
dona  1.' 

I  to  explain. 
I        :t  and  :i'  show  n  of  Ilia  Inter. 

'.  "f  the  handle,  with  ii 
cal  cytlnder,  i.',  of  the  key.    The  curri 
according  i"  Il  i 

i         \  iv.    We  here,  how 
■ 

.  yllndor,  i '.  Bga.  81  and  8*,  1 
Inclined  I  a  Ith  the 

.  .  lindi  r.  i '.  aaaumea  a  dlflbrenl  aj 
in  ilii-.  i  I         ■  itruction,  h..»< 

follows  : — To  obtain  any  |*.int  iii  the  curve,  «.■  proi 

■  ample,  .In." 
t..  the  axel  of  tho  cylinders,  tlii-«  puu  ■ 
tlir..iiL'h  the  In  • 

I  ■  i the  vertical  |>r.> 

• 
on  h  ii,  th.   hi 


BOOK  OF  INDUSTRIAL  DESIGN. 


line,  d  e.  drawn  through  the  poiut,  ft',  represents  the  intersection 
of  the  plane  with  the  horizontal  cylinder,  ft  ft',  being,  of  course, 
measured  from  its  rxis.  It  will  be  seen  that  the  line,  d  e,  is  cut 
by  the  vertical  lines,  a" /and  e  g,  in  the  points,  d,  e,  which  lie  in 
the  curve  sought ;  and  the  same  construction  will  apply  to  every 
other  point  in  the  curve,  dbec. 

181.  Figs.  4  and  5  represent  the  intersection  of  an  elliptical 
cylinder  wilh  a  right  cone  of  circular  base,  corresponding  to  the 
external  conical  surface,  A,  of  the  cock,  at  its  junction  with  the 
shoulders,  d.  Fig.  5  is  a  plan,  looking  on  the  cock  from  below, 
and  which  shows  the  horizontal  projection  of  the  intersectioual 
curves. 

The  solution  of  the  problem  requiring  the  determination  of  these 
curves  consists  in  applying  a  method  already  given — namely,  in 
taking  any  horizontal  plane  which  cuts  the  cone,  so  as  to  present  a 
circular  section  on  the  one  hand,  and  the  cylinder  in  two  straight 
lines  on  the  other — the  points  of  intersection  of  these  straight  lines 
with  'lie  circle  representing  the  section  of  the  cone.  Thus,  by 
drawing  Ihe  plane,  c  d,  fig.  4,  we  obtain  a  circle  of  the  diameter,  c  d, 
which  is  projected  horizontally,  as  with  the  centre,  o,  fig.  5;  we 
have  also  two  generatrices  of  the  cylinder,  both  projected  in  the 
vertical  plane  in  the  line,  a  A,  and  in  the  horizontal  plane  in  the  lines, 
a'  ft'  and  a-  ft3.  Having  drawn  the  semibase  of  the  cylinder,  d  e,  as 
at  d"/e',  and  having  taken  the  distance,/ g,  fig.  4°,  and  set  it  off,  in 
fig.  5,  from  the  axis,  as  from  g'  to  a',  and  to  a2,  we  thereby  obtain 
the  generatrices,  a'  b'  and  a  '  6s,  which  cut  the  circle  of  the  dia- 
meter, c'  d',  in  the  four  points,  ft'  i',  which  are  squared  across  to, 
and  projected  in,  the  vertical  plane  in  the  points,  ft,  i.  In  the 
same  manner  we  obtain  any  other  points,  as  m,  n;  k  I  being  the 
plane  taken  for  this  purpose.  The  extreme  points  of  the  curve 
are  obtained  in  a  very  simple  and  obvious  manner,  as  /,  g,  r,  s, 
being  the  points  of  intersection  of  the  extreme  generatrices,  or 
■  the  outlines  of  the  two  solids.  With  regard  to  the  points,  t,  u, 
which  form  the  apices  of  the  two  curves,  their  position  may  be 
obtained  from  the  diagram,  fig.  4",  by  drawing  from  the  point,  s, 
which  would  be  the  apex  of  the  entire  cone,  a  tangent,  s  t,  to  the 
base,  d'  fe',  of  the  cylinder,  and  projecting  the  point  of  contact,  t, 
in  the  line,  x  y,  representing  a  plane  cutting  the  cone,  which  must 
be  projected  in  the  horizontal  plane.  Then,  making  g'  x',  fig.  5, 
equal  to  t  r,  fig.  4',  and  drawing  horizontals  through  x',  their 
intersections,  (  u',  with  the  circular  section  of  the  cone,  will 
be  the  points  sought,  which  are  accordingly  squared  over  to 
fig.  4.  The  operations  just  described  are  analogous,  it  will  be 
observed,  to  those  employed  in  obtaining  the  intersection  of  two 
cylinders. 

If,  in  the  case  of  the  cone  and  cylinder,  the  latter  had  been  one 
of  circular  instead  of  elliptical  base,  as  is  frequently  the  case,  still 
the  construction,  as  a  little  consideration  will  show,  must  be  pre- 
.  isoly  the  same,  and  the  resulting  curves  would  be  analogous — that 
i>  when  the  diameter  of  the  cylinder  is  less  than  that  of  the  cone 
at  Jie  part  where  it  meets  the  lowTest  generatrix  of  the  cylinder; 
the  curves,  however,  assume  a  different  appearance  when  the  dia- 
meter of  the  cylinder  exceeds  this,  as  is  shown  in  figs.  6  and  7. 
In  this  case  the  intersections  are  represented  by  the  curves,  sir 
and  p  u  q;  the  method  of  obtaining  these  is  fully  indicated  on  the 
diagrams. 


185.  The  opening  or  slot,  H,  cut  through  the  key  of  Ihe  stop- 
cock,  is  generally  rectangular,  rather  than  circular,  or  similar  to 
the  tubular  portions  of  the  cock.  The  object  of  this  shape  is  to 
make  the  key  as  small  as  possible,  and  yet  retain  the  required 
extent  of  passage.  This  rectangular  opening  gives  rise,  in  Bg.  2*, 
to  the  intersectional  curves,  a  b,  c  d,  which  are  portions  of  the 
hyperbola,  resulting  from  the  section  made  by  a  plane,  cutting  tin- 
cone  parallel  to  its  axis.  The  operations  whereby  they  are  deter- 
mined are  indicated  in  figs.  10,  11,  and  12. 

To  render  the  character  of  the  curve  more  apparent,  we  have, 
in  these  figures,  supposed  the  generatrices  of  tho  cone  to  make  a 
greater  angle  with  the  axis  than  in  fig.  2'.  The  line,  a  ft,  ivprc- 
sents  the  vertical  plane  in  which  the  curve  of  intersection  lies. 
It  is  evident  that,  if  we  delineate  a  series  of  horizontal  plains,  as 
c  d,  ef,  g  ft,  i  k,  fig.  10,  we  shall  obtain  a  corresponding  series  of 
circles  in  the  horizontal  projection,  these  circles  cutting  the  plane, 
a  b,  in  the  points,  /',  m',  n',  p',  &c.  These  points  are  squared  over- 
to  the  vertical  projection,  fig.  10,  giving  the  points,  I,  m,  n,  p  ;  and 
the  apex,  o,  of  the  curve  is  obtained,  by  drawing  in  the  plan, 
fig.  12,  with  the  centre,  s,  a  circle  tangent  to  the  plane,  a  b,  and 
then  projecting  this  on  the  vertical  plane,  fig.  10,  as  shown. 
From  these  diagrams,  it  is  easy  to  see  that  the  opening,  h,  will  be 
partly  visible  when  the  key  is  seen  from  below,  as  in  fig.  2'. 

186.  Figs.  8  and  9  represent  the  vertical  and  horizontal  pro- 
jections of  the  nut,  a,  which  secures  and  adjusts  the  key  in  its 
socket.  This  nut  is  hexagonal,  being  terminated  by  a  portion  of 
a  sphere,  the  centre  of  which  lies  in  the  axis  of  the  prism.  Each 
of  the  facets  of  the  prism  cuts  the  surface  of  the  sphere,  so  as  to 
present  at  their  intersection  portions  of  equal  circles,  which  should 
be  determined  in  lateral  projection.  The  diameter  of  the  sphere 
is  generally  three  or  four  times  that  of  (he  circle  circuml 
the  nut,  but,  to  render  the  curves  more  distinct,  we  have  adopted 
a  smaller  proportion  in  the  case  under  examination.  Tin-  sphere, 
y,  is  represented  by  two  circles  of  the  radius,  o  a;  and  the  nut  by 
an  hexagonal  prism,  the  axis  of  which  passes  through  the  eentre  of 
the  sphere.  The  anterior  facet,  a'  b',  of  this  nut,  cuts  the 
so  as  to  show  a  circle  of  the  diameter,  c'  d'.  This  circle,  projected 
vertically  on  fig.  8,  cuts  the  straight  lines,  a  e  and  hi,  ni  the 
prism,  in  the  points,  a  and  b ;  and  the  portion  of  the  circle  com- 
prised between  these  two  points,  consequently,  represents  the 
intersection  of  this  facet  with  the  sphere.  The  other  two  facets, 
a  g'  and  b' h',  which  are  inclined  to  the  vertical  plane,  also  cut 
the  sphere,  so  as  to  produce,  at  their  intersection  with  the  surface, 
arcs  of  equal  radii  with  that  of  the  facet,  a  4.  From  their  incli- 
nation, these  ares  become  slightly  elliptical,  being  comprised,  on 
the  one  hand,  between  the  points,  a  and  g,  and  ft,  ft,  on  tb 
The  summits  of  these  ellipses  are  obtained  by  drawing  horizontal 
lines  tangential  to  the  arc,  a  ft,  and  cutting  it  in  the  points,  '..  /. 
by  perpendiculars  drawn  through  the  middle  of  the  lateral  facts. 
In  practice,  it  is  quite  sufficient  to  describe  circular  arcs.  \>.  ssing 
through  the  points,  g,  k,  a,  and  ft,  I,  ft. 

We   have   already   seen,    in    reference   to    Plate  XIV..  that    Ihe 
intersection  of  a  right  cylinder  with  a  sphere,  through  thi 
of  which  its  axis   passes,  gives  a  circle  projected  laterally  as  a 
straight  line.     Thus,  the  opening  o',  which  passes  through  the  nut. 

being  cylindrical,  produces,  by  its  intersection  with  the  sphere,  a 


Tin:  i 


eirc!*  of  the  diameter,  aV  W,  in  the  j Jan.  projected  vertically  in  the 
airtight  fine,  m  n. 

-•  jmfiml—  lb*  ■— lognea  operations  required  to  .!- 
the  mm  int«wrti«iiu  when  the  nnt  ia  wn  with  ooe  of    the 
angles  fat  the  centre,  and  only  two  faceU  visible,  aa  represented  in 

fi«c  >•• 

The  eluptfc  ranre,  b'  /»  a',  eoniwpiinitinp  I  .  H.  tim-t 

obrlu— ly  he  eomprU-  tal  line* 

pansinr;  through  theae  points,  and  an  are  ia  drawn  thrun. 

ay  here  observe,  that   the  proficient  draughtsman  will, 
doabtleaa,  deem  it  unnwi— it.  swept  in  extraordinary  cases,  to 
Ut    atirh    minute    details    <.|"  !  far  the  \ari.-u* 

llllllaw I tiniial  runes   as  turn 

:.  and  the  appesranco   prescntnl   by 
different    experimental  All   draughtsmen,   ) 

will  find  that  some  practice  in  "rtrtrilihig  tl  ntetfon 

of  the  various  cunes,  accor 
rolea  laid  down,  will  t- 
them,  from  possessing  a  thorough  theoretical  knowledge  of  the  n-la- 

.irious  forma  of  solids  to  eat 
much  ix-an  r  Initli,  wlien,  at  a  more  advanced  stage,  they  r< 
the  aid  uf  such  constructive  | 


\\U  PRACTICAL  DATA 


All  liquids  become   change.) 
I«  ratlin-  is  sul! 

- 

Ttoe  prasauri 

in  a  vacuum,  a  i 

cury  3"  -   iijiial  to  a  u 

IB  'I...  par  ■qoara  mek 

Thus,  taking  the  square  inch  as  tl  rtirial  measure- 

ment, the  pre.-  ,  of  the  atvain 

also  equal  to  15  lbs. 

ntaining  vessel  is  hermetically  closed,  as  in  a 

if  the  t  ^ 

. 
not  loin;.'  directly  pr-  : 
The    t.  n-i..n    or    <■> 

al  the  pressor, 
volume    of  II  • 
one   enj  Mie  quantity  q) 

half  the  sjiace  at  a  pressure  ol 


TATiLE   OF    PRESSURES,   TEMPEBATfRES,    WEIGHTS,    ASD    VOLfMES  OF   STEAM. 


PrMMrw  is 

Pi— mn  is  It><-he« 

runs  r»r  So,ssr« 

Tfii>i»r*lMri 

Traiprretarj 

'     .'.<   uUr  Fu* 

Vuloai.  •*  .  r...»a 

*'—'•'"'"- 

of  Maresry. 

Fahr*&h«tu 

rata. 

of  8USBU 

af  M..m 

Lb. 

100 

219 

375 

160 

450 

119-4 

175 

■Ji:t 

117  1 

1   '..'-1 

250 

3375 

350 

1  1777 

870 

I  9771 

300 

90-0 

1 

•J-  i 

1377 

3  50 

4-00 

1  1  •.  1 

4  50 

135-0 

1  19  l 

6-00 

1600 

650 

114 

l  7494 

■«716 

6-00 

1800 

n  oo 

310  0 

331 

•J  1777 

800 

B40-0 

19 

141 

179-1 

•J  1669 

•4071     . 

the  aaaktance  of  this  table,  wo  esj 

a:— 

First  F.xamjit. — What  is  the  amount  of  ■team  pressor 
on  a  piston  of  10  inches  diai 

■'■■■grcest     It  will  I*.  Ntn  that  the  pressure  corresponding 
is  equal  to  three  atmospheres,  or  to  45  lbs.  per  aquaro 

The  area  of  a  bJbJm  "f  in  inches  in  diameter  is  equal  to 
10*  x  -7854  =  78-51  sq.  b 


78  54  •   18       Nt4  3  Ids. 

Thn-    ■ 

indlng  t"  Km  given  temperature,  and  multiply  It  by  the 
Second  F.ramflr.—  \\  !  .luring 

\\  .    :      •     '-'.lin  the  volume  •  <|>  ii'l.-l, 
\- 


x  3  —  19  635  cubic  feet. 


BOOK   OF   INDUSTRIAL   DESIGN. 


At  a  pressure  of  three  atmospheres,  a  cubic  foot  of  steam  weighs 
1-0058  lb. ;  consequently, 

19-635  x  1-0058  =  1975  lbs. 

To  solve  this  problem,  then,  we  ascertain  the  volume  expended 
in  cubic  feet,  and  multiply  it  by  the  weight  corresponding  to  the 
given  temperature,  or  pressure — the  product  is  the  weight  in 
pounds. 

UNITY   OF   HEAT. 

188.  With  a  view  to  facilitate  various  comparisons  connected 
with  the  subject  of  steam,  the  French  experimentalists  have 
adopted  the  term  calorie,  or  unity  of  heat.  This  is  defined  as  the 
amount  of  heat  necessary  to  raise  the  temperature  of  a  kilogramme 
(=  2-205  lbs.)  of  water,  one  degree  centigrade. 

Thus,  a  kilogramme  of  water  at  25°  contains  25  unities  of  heat ; 
and,  in  the  same  manner,  60  kilog.  of  water  at  50°  contains 
50  x  60  =  3000  unities. 

The  number  of  unities  of  heat  is  obtained  by  multiplying  its 
weight  in  kilogrammes  by  the  temperature  in  degrees  centigrade. 

The  amount  of  heat  developed  by  different  descriptions  of  fuel 
varies  according  to  their  quality,  and  according  to  the  construction 
of  the  furnaces. 

According  to  M.  Pcclet,  the  mean  quantity  of  heat  developed 
by  a  kilogramme  of  coal  is  equal  to  7500  calories,  or  unities  of 
heat. 

According  to  M.  Berihier,  that  developed  by  a  kilogramme  of 
wood  charcoal  varies  from  5000  to  7000  unities. 

In  the  following  table  will  be  found  the  results  of  experiments 
with  different  descriptions  of  fuel : — 

Table  of  the  Amount  of  Heal  developed  by  one  Kilogramme  of  Fuel. 


Description  of  Fuel. 

Number  of 
unities  of  heat 
developed  by 

Quantity  of 

steam  practically 

obtainable  from 

1  kdog. 

6000  to  7000 
6000 
7500 
4800 

3000 

1500 
3600 

2800 

5800 

Kilo?. 
5-6    to  6 

7-       "  8 

575   "  7 

Drv  Turf, 

Common  Turf,  containing  20  per 

:ent 

1 

1-8     "  2 

« 

Dry  Wood  of  all 
Common    wood, 

3-7 

containing   20 

per 

I 

27 

Tint'  Charcoal,. . 

28    to  3 

In  the  last  column  of  this  table,  we  have  given  the  quantities 
of  steam  produced  by  the  combustion  of  one  kilogramme  of  fuel, 
being  such  as  are  practically  obtainable  in  apparatus  most  com- 
monly met  with. 

Example. — What  is  the  quantity  of  coal  necessary  for  the  sup- 
ply of  a  furnace  intended  to  produce  250  kilog.  of  steam  ' 

The  average  produce  of  1  kilog.  of  coal  being  6-5  kilog.,  we 
have 

250 

-r-r  =  84  kilog.  of  coal. 

189.  The  boilers  in  which  the  steam  is  to  be  produced,  may  be 


of  the  shape  represented  in  figs.  4  and  5,  Plate  XIV. — that  is, 
cylindrical,  and  terminated  by  hemispheres.  They  tire  frequently 
accompanied  by  two  or  three  tubular  pieces  in  connection  with  tlio 
main  portion  of  the  boiler  by  pipes.  Boilors  answering  to  tliis 
description  are  termed  French  boilers,  being  of  French  origin  ;  they 
are  found  very  effective,  and  are  much  used  in  the  manufacturing 
districts  of  England.  These  boilers  are  made  of  plates  of  wrought- 
iron,  the  thickness  of  which  varies,  not  only  according  to  the  sizo 
of  the  boilers,  but  also  according  to  the  pressure  at  which  it  is 
intended  to  produce  steam. 

The  proper  thickness  for  the  plates  of  cylindrical  boilers  may 
be  determined  by  the  following  formula,  which  is  the  one  adopted 
by  the  French  Government  in  their  police  regulations  : — 


_  18  x  d  x  p 


+  3; 


where 


T  =  thickness  in  millimetres; 

d  =  diameter  of  boiler  in  metres ; 

p  =  pressure  in  atmospheres,  less  one. 

The  rule  derivable  from  the  formula  is — . 

To  multiply  the  effective  pressure  of  fJie  steam  in  atmospheres 
by  the  diameter  of  the  boiler,  and  by  the  constant  18,  dividing  the 
product  by  10,  and  augmenting  the  quotient  by  3,  which  will  give 
the  thickness  in  millimetres. 

To  simplify  these  calculations,  we  give  a  table  showing  the 
thickness  proper  for  boiler  plates,  calculated  up  to  a  diameter 
of  2  metres,  and  to  a  pressure  of  8  atmospheres  above  tin-  atmo- 
sphere : — 

Table  of  Thicknesses  of  Plates  in  Cylindrical  Rollers. 


Diameter 
of  Boiler. 

Pre 

ssure  of  Steam  in  Atmoaphe 

2. 

3. 

4. 

5. 

6. 

7. 

8. 

Metres. 

Millim. 

Millim. 

Millim. 

Millim. 

Millim. 

Millim. 

Millim. 

•50 

3-9 

4-8 

5-7 

6-6 

7-5 

8-4 

9-3 

•55 

4-0 

5-0 

6-0 

7-0 

7-9 

8-9 

9-9 

•60 

41 

5-1 

6-2 

7-3 

8-4 

9-5 

10-5 

■65 

4-2 

5-3 

6-5 

7-7 

8-8 

lii-ii 

11-2 

•70 

4-3 

5-5 

6-8 

8-0 

9-3 

10-5 

1 1-8 

•75 

4-3 

5-7 

7-0 

8-4 

9-7 

111 

12-4 

■80 

4-4 

5-9 

7-3 

8-8 

10-2 

11-6 

131 

•85 

4-5 

61 

7-6 

91 

10-6 

12-2 

13-7 

•90 

4-6 

6-2 

7-9 

9-5 

111 

12-7 

14-3 

•95 

4-7 

6-4 

8-1 

9-8 

1 1-5 

13-3 

15-0 

1  <>0 

4-8 

6-6 

8-4 

10-2 

12-0 

13-8 

15-6 

1-10 

5-0 

7-0 

8-9 

10-9 

12-9 

1  III 

" 

1-20 

52 

73 

9-5 

11-6 

13-8 

10-0 

" 

1-30 

5-3 

7-7 

10-0 

124 

14-7 

" 

" 

1-40 

5-5 

8-0 

10-6 

131 

15-6 

" 

" 

1-50 

5-7 

8-4 

111 

13-8 

" 

" 

" 

1-60 

5-9 

8-8 

11-6 

11-5 

" 

" 

" 

1-70 

61 

91 

12-2 

152 

" 

" 

" 

i-flb 

6-2 

9-5 

12-7 

160 

" 

" 

" 

1-90 

6-4 

9-8 

13-3 

" 

" 

" 

" 

2-00 

6-6 

10-2 

138 

" 

" 

11 

To  suit  English  measures,  the  foqjula  is — 
18  xd  x  p 


10,000 


+  -1182. 


Tin:   r  i>it  \ii.iii 


And  lure, 

--in  Inches; 
J  =  diameter  in  Inches  ; 
•  =  prvaaure  in  »Unu»}4nn-»,  low  one. 

Ill:  ATI**    mi 

d  ili.il  a  square  metro 

.in  per 

h<>ur,  »  indlical,  with  or 

. 

l<i    I-  y    in.lwl.<l    tli.it    whi.h    is    .iirft-lly 

• 
fn>m  tli. 

si  tin-  production  of  -' 

hbalf  "r  a  third  of  tbja 
I  t.i  tin-  direct  action  "f  tin-  tin-,  which  will  give, 
f..r  the  whole  b 

In  tl.  "■  principal  dimension! 

I  ■■- ■  -  j-  a.  i  ol  i  i  era  ■•!  the  French  dcecrip- 
ti.ui — that   in,   cylindrical    with   two 

dp 

1 1  ■   I!  I  /'       •  fi-r  a 

/'  I 


L»iw1h  nf 

1 

■he  Tuba. 

•  M. 

II. 

H. 

at 

- 

I 

4 

•J   in 

A 

'.' 

In 

R 

10 

10 

10 

111 

li 

1" 

1<I 

111 

10 

1" 

111 

* 

10 

111 

111 

11 

10 

1 

11 

111 

.without  additional  tubes,  the  water  ahonld 

lwo4hirda  of  tin-  whole  apace,  and  in  boilers,  with  the 

i  occupy  aboul  one-half  the  main  cylindrical  body 

I    til   till'    tiling. 

Iii  order  that   (he  with  it  small 

lich  sction   is  termed  "ftriminii"  the  Im.iI.t 

i»  anriB  ■  dome,  In  which  the 

;..rt  of  Which  II 

thrown  op  by  the  obullitioff 

'  '  '■'■  ■    r  n  cylindrical 

e>-  'i"i'  "f 

be  luat- 
in\i  surface  13  sq.  tn.,  par  li 


I  x  6  =  7*  sq.  nx^total  heating  surface. 
1  tliat 


7-8  aq.  m.  =  L 


J        ,         i  -,  K 
^r  =  L  x  — — , 

3  3 


Ji  nought,  nn  I    El  the  I 
=   '4  m.;   so  that,  nulmtiluting   fur  K   sud    It    : 


7-8  aq.  m.  =  L  x  314  x  -4  x  —  =  L  > 


L  = 


•    i  ■ .".  ■ 


An  it  may  In-  an  11  i  fin  watca. 

DA,   this    may    : 

I 
Tin-  boQar  being  terminated  by  bamisphari  of  the 

cylindrical  iHirtiuii  will  be  aqua]  to 

—  (4  x  2)  =  385. 

iH   bare,  th.n,  fur  the  \  to  iho 

cylindrical  portfoo — 


iitnl  for  thai  of  tl  .J  ends — 

2^ 

The  whole  volume  of  •>■  |nently, 

I  189 1  ihl 
The  remainder  of  the  volume,  whi 
is  obviously 

2 

inlill'T, 

II' 
This  result  might  bave  been  obtained  by  the  following 
formula  i — 

t 
.) 


=  -731  cubic  ■ 


v  =  L  x  i  i;    i 


R'  = 


14  , 

191.  Wo  I"  r.    quote  the  portion  of  the  n 
the  French  Governmi  nt,  relal 
what  condition  I 

of  public  .-.ili  iv,  and 
• 

ire  divided  Into  f"iir  1 1 

"Tli.  the  boiler,  ine'ndlng  thai  of  the  tnl 

mere  \*-  any,  must  b 

ii  i  in  it  ati  tnd  tl 

two  quantitlea  multiplied  Into  each  other.  • 

••  it  tin-  product  <  n 

..II.  lull 

:  fifteen.    <  »f  tin-  third,  whan  mora  than  tl. 
fourth,  when  uol    i  <i 

••  If  two  in  i  to  work  in  corn 

:iini.'ati..|)   wr: 


BOOK  OF   INDUSTRIAL  DESIGN. 


81 


term  taken  to  represent  the  capacity  "must  be  tho  sum  of  the 
capacities  of  each. 

"  (34.)  Steam-boilers  of  the  first  class  must  bo  stationed  outside 
of  idl  dwelling-houses  or  workshops. 

"  (35.)  Nevertheless,  in  order  that  tho  heat,  which  would  other- 
wise be  dissipated  by  radiation,  may  bo  better  economised,  the 
officer  may  allow  a  boiler  of  the  first  class  to  be  stationed  inside  a 
workshop,  provided  this  does  not  form  part  of  a  dwelling-house. 

"(36.)  Whenever  there  is  less  than  10  metres  in  distance 
between  a  boiler  of  the  first  class  and  a  dwelling-house  or  public 
road,  a  wall  of  defence  must  be  built,  in  good  and  solid  masonry, 
and  1  mitre  thick.  Tho  other  dimensions  are  specified  in  article 
41:  This  wall  of  defence  must,  in  all  cases,  be  distinct  from  the 
masonry  of  the  furnaces,  and  separated  from  it  by  a  space  of  at 
least  50  centimetres  in  width.  It  must,  in  a  like  manner,  be 
separated  from  the  intermediate  walls  of  the  neighbouring  houses. 

"  If  the  boiler  be  sunk  into  the  ground,'  in  such  a  manner  that 
no  part  of  it  is  less  than  1  metre  below  the  level  of  the  ground, 
the  wall  of  defence  shall  not  be  required,  unless  the  boiler  is  within 
5  metres  of  a  dwelling-house  or  of  the  public  road. 

"  (38.)  Steam-boilers  of  the  second  elass  may  be  stationed  inside 
a  workshop  which  does  not  form  part  of  a  dwelling-house,  or  of 
a  factory  or  establishment  consisting  of  several  stories. 

"  (39.)  If  a  boiler  of  the  second  elass  be  within  5  metres  from  a 
dwelling-house  or  the  public  road,  an  intermediate  wall  of  defence 
shall  be  erected,  as  prescribed  in  article  36. 

"(41.)  The  authority  given  by  the  inspecting-offieer  for  boilers 
of  tho  first  and  second  class,  shall  indicate  the  situation  of  the 
boiler,  its  distance  from  dwelling-houses  and  the  public  roads,  and 
shall  determine,  if  there  be  space  enough,  the  direction  to  be  given 
to  the  axis  of  the  boiler. 

"  This  authority  shall  also  specify  the  situation  and  dimensions, 
as  to  length  and  height,  of  the  wall  of  defence,  where  this  is 
required,  in  conformity  with  the  above  regulations. 

"  In  determining  these  dimensions,  regard  must  be  had  to  the 
capacity  of  the  boiler,  to  the  pressure  of  the  steam,  as  well  as  to 
all  circumstances  tending  to  make  the  boiler  more  or  less  danger- 
ous or  inconvenient. 

"  (42.)  Steam-boilers  of  the'  third  class  may  be  stationed  in 
workshops  which  do  not  form  parts  of  dwelling-houses,  and  it  is 
not  necessary  to  erect  a  wall  of  defence. 

"  (43.)  Steam-boilers  of  the  fourth  class  may  be  stationed  in 
any  workshop,  even  if  tins  forms  part  of  a  dwelling-house. 

"  In  this  caso,  the  boilers  must  be  furnished  with  an  open 
manometer. 

"  (44.)  Tho  furnaces  of  steam-boilers  of  the  third  and  fourth 
class  shall  be  entirely  separated,  by  a  space  of  at  least  50  centi- 
metres, from  any  dwelling-house." 

According  to  these  regulations,  a  boiler  of  the  dimensions  taken 
fir  illustration,  and  supposing  tho  maximum  pressure  to  be  3 
atmospheres,  would  be  in  the  second  class,  for — 2-203  x  3  = 
6-609,  winch  is  below  7. 

Second  Example. — What  should  be  the  dimensions  of  a  cylin- 
drical boiler,  with  two  additional  tubes,  intended  to  supply  an 
engine  of  16  horses  power,  tho  diameter  of  the  main  body  being 
•9  m.,  and  that  of  the  tubes  -45  m.  ? 


Assuming  1-2  sq.  m.,  per  horse  power,  fur  the  heating  surface, 
wo  shall  havo  1-2  X  16  =  192  sq.  m.,  for  the  entire  heating  sur- 
face. Half  of  tho  surface  of  the  main  cylinder  of  the  boiler,  and 
three-fourths  of  that  of  the  tubes,  is  the  best  disposition  of  this 
heating  surface.     These  data  give  riso  to  tho  following  formula  :— 

, .  „  2«  R  x  L  ,  3 

19:2  sq.  m.  = +  r2*xLx2x  —  = 

J,  4 

n  R  L  4-  3rt  r  L— . 

L  here  represents  tho  length  of  tho  boiler  and  tubes,  which  is 

the  only  unknown  term. 

Substituting  for  R  and  r  their  numerical  values,  -45  and  -225, 

we  have — 

19-2  sq.  m.  =  3'14  x  -45  x  L  +  3  x  3-14  x  -225  x  L;  or 

19-2  sq.  m.  =  L  (3-14  x  -45)  4-  3  x  3-14  x  -225  = 

L  (1-413  +  2-12); 

whence, 

19-2  19-2 

3-533 


=  5-43  m. 


1-413  +  212 

Thus,  the  total  length  of  the  boiler  is  5-43  m.,  but  the  ends 
being  hemispherical,  the  length  of  the  cylindrical  portion  is 
equal  to — 

5-43  —  -9  =  4-53  m. 
The  tubes  usually  project  in  front  of  the  main  body,  to  a  dis- 
tance of  about  50  centimetres;  but,  for  convenience  in  constructing 
the  return  flues,  they  do  not  extend  as  far  back,  so  that  they  aru 
of  about  the  same  length  as  the  main  body. 

192.  In  distillery  boilers,  a  horse  power  is  understood  to  mean 
the  capability  of  evaporating  25  kilogrammes  of  water  in  an  hour. 
Thus,  a  boiler  of  10  horses  power  should  be  capable  of  evaporating 
250  kilog.  of  water  in  that  time.  Now,  assuming  l-f2  sq.  m.  of 
heating  surface,  per  horse  power,  for  a  steam-engine,  we  should 
only  have  an  evaporation  of  from  18  to  20  kilog.  per  hour,  per 
horse  power,  and  per  square  metre  of  heating  surface. 

DIMENSIONS   OF   FIRE-GRATE. 

193.  In  practice,  1  square  metre  of  grate  will  burn  from  40  to 
45  kilog.  of  coal  per  hour.  Thus,  a  boiler  intended  to  produce 
280  kilog.  of  steam  per  hour,  will  require,  for  this  purpose — 
assuming  that  1  kilog.  of  coal  produces  6-65  of  steam — 

280 

'.  „  =  43  kilogrammes  of  coal ; 
oo5 

and  tho  furnace  of  tins  boiler  should  have  a  grate,  measuring  1 

square  metre. 

Tho  grate-bars  are  generally  of  cast-iron,  of  from  30  to  35 
millimetres  in  width,  but  having  between  them  a  space  of  only 
7  or  8  millimetres,  so  that  tho  intervals  only  occupy  a  fourth  or 
a  fifth  of  the  whole  area. 

It  has  been  found  that  greater  strength  and  durability  is 
obtained  by  making  the  bars  straight  above,  and  strengthened  by 
parabolic  feathers  below. 

CHIMNEYS. 

194.  The  height  of  chimneys  is  very  variable,  and  cannot  bo 
subjected  to  any  fixed  rule.  The  cross  section  at  the  summit 
depends  upon  the  size  of  the  grate,  and  is  generally  about  a  sixth  of 


TJIK    I 


this.     In    the    f.41owing   application   will   be  found    calculations 
respecting  chkuncy*,  and  examples  of  the  various  rule*  « 

Ami 

-opoae   calrula'in.-    the  dimensions  i.f    the  funu. 
-  an  engine  of  8  bone*  poi 
example,  to  be  worked  on  the  higb-preasure  system,  consuming,  aa 
a  maiimiim,  5  kilogramme*  of  coal,  :  -.  par  hour,  the 

amount  of  beating  aurfare  being  taken  at  1  Ul  eq.  in.,  p 
power. 

For  8  horaea  power,  the  boa' 

. 
Da,  »e  have— 

:  218-88  kilog.  of  steam. 
Aa  5  kilog.  of  steam  are  produced  by  1  Uog.  of  coal,  I 

— s— =  «-8k;: 

representing  the  quanti:;,  r  hour. 

TT>e  grate  ;.- 
that  one  square  decimetre  L>  sufficient  fur  1*3  Idlog.  par  hour,  will 


l  J 


=  36  square  dt  • 


rth  of  this  area  to  U  .-sage  of  air. 

-  to  calculate  the  cross  sectional  ana  of  the 
must   remark,  that    1  - 

of  coal; 
,'iiro 
43  8  x  18  =  "7881  . 

I  of  its 
>(.-  acid  "a*  nii- 

f  to  M.  P(     •  *.  at  tlie 

•  hoar.    If  wi  drrfcV  - 

ohlain  the  quantity  which  em-apes  per  second  ;  nan 
1< 


aaaume,  aa  is.  0  ]  r..|~.r- 

dl  of  the  aa*  -  inula:— 

\ 
In  the  case  II   =  oj  ,„    „  j.  th.  i-..n-t.int 

r  numerical  ij 
\         '  ■   •    (300  —  15)  =  91. 

■gnttM  that  t  ,n  theehfanni 

actual 
rale.  I  _.,r, 

T        It  7  m. 
•be  rate  .-.,  that  time, 


i 


•hall  obtain  the  croa*  sectional  area  proper  for  the  upper  part  of 
the  chimney  ;  as  thus— 

Tliu«  is.  supposed  to  be  aquare,  will  only 

internally,   something   leas   than   tw 
metres  each  way  at  t:  ■  ■  mini- 

mum dimension,  and  il  '  .Traler  dimen- 

square, 

• 
-    in     manufactories.     A    dnin. 

should   I 


Table 

/ 1  I  triers  of  Safety 

1 

EiUst  »f 

Fiwwi  Is  AiawybirM 

% 

■i\ 

S 

»t 

! 

*U 

*/ 

"/. 

"/ 

»/ 

*  1 

"/ 

"/.. 

■  / 

•v  *■ 

1 

it 

11 

9 

1 

13 

4 

11 

3 

66 

36 

0 

61 

II 

7 

66 

39 

36 

8 

39 

I 

64 

II 

41 

36 

10 

79 

66 

17 

43 

It 

83 

68 

60 

43 

33 

11 

66 

63 

49 

It 

M 

67 

61 

41 

33 

96 

33 

36 

ia 

63 

63 

39 

66 

17 

83 

74 

66 

If 

87 

76 

68 

63 

68 

90 

64 

60 

41 

HI 

93 

66 

61 

•J  I 

111 

68 

63 

117 

97 

84 

76 

69 

64 

II 

99 

86 

66 

38 

67 

39 

90 

69 

60 

91 

63 

63 

73 

64 

111 

97 

136 

-1 

66 

84 

69 

149 

83 

101 

86 

101 

63 

111 

lo| 

101 

60 

IS! 

73 

•ceea*.  '  .;/j,  alarm  ir/i 

.1    instrument    which   MTTM  to  indicate  tho 
the  In.iler  in  al 


BOOK  OF   INDUSTRIAL  DESIGN. 


63 


The  float  serves  to  indicate  the  level  of  the  water,  and  the 
whistle  to  give  the  alarm  when  the  water  is  much  below  the  pro- 
per level. 

The  safety  valve  provides  fm  exit  for  the  steam  when  the  pres- 
sure is  too  high. 

We  have  given  a  drawing  of  one  at  fig.  4,  Plate  XI.  Their 
diameters  vary  with  the  dimensions  of  the  boilers  and  the  pres- 
sure of  the  steam. 

The  regulations  of  the  French  Government  contain  the  following 
rules  and  the  above  table  for  their  determination.  To  find  the  proper 
diameter  for  the  safety  valve,  the  heating  surface  of  the  boiler, 
expressed  in   square   metres,  must  be  divided  by  the  maximum 


pressure  of  steam  intended  to  be  maintained,  expressed  in  atmo- 
spheres, previously  diminished  by  the  constant  "412:  the  square 
root  of  the  quotient  being  extracted,  is  to  bo  multiplied  by  :2-(J, 
and  the  product  will  be  the  diameter  sought,  expressed  in  centi- 
metres.    This  rule  may  be  put  as  a  formula,  thus: — ■ 


2-6 


V^T 


11  2 


where  d  is  the  diameter  of  the  valve  in  centimetres,  s  the  healing 
surface  of  the  boiler,  including  both  tire  and  Hue  surface,  expressed 
in  square  metres,  and  n  the  number  expressing  tho  pressure  iu 
atmospheres. 


CHAPTER    V. 


THE   STUDY   AND    CONSTRUCTION   OF   TOOTHED   GEAR. 


196.  Toothed  gear  is  a  mechanical  expedient,  universally 
employed  for  the  transmission  of  motion.  It  is  met  with  of  all 
proportions,  from  the  minute  movements  of  the  watch,  to  the 
gigantic  fittings  of  manufacturing  workshops.  Toothed  gear  is 
generally  constructed  with  a  view  to  the  following  principle  of 
action — that  the  lateral  acting-surfaces  develop  the  same  arc  during 
the  same  duration  of  contact,  whilst  their  angular  velocities 
vary  inversely  as  their  diameters.  By  the  angular  velocity  of 
any  body,  turning  about  a  centre,  is  meant  the  angle  passed 
through  by  tho  body  in  a  unit  of  time ;  whilst  the  real  or  linear 
velocity  of  any  point  is  the  space  passed  through  by  this  point, 
whether  the  direction  of  motion  be  rectilinear  or  circular.  Thus, 
various  points  on  a  crank,  taken  at  different  distances  from  the 
centre  of  the  shaft,  have  all  the  same  angular  velocity,  whilst  their 
actual  velocity  differs  considerably,  because  of  their  respective 
distances  from  the  centre.  It  is  the  same  with  a  pendulum,  which 
vibrates  through  an  angle,  or  has  an  angular  motion  about  its 
centre  of  suspension.  The  angular  velocity  of  a  body  is  greater, 
as  the  angle  passed  through  in  the  same  time  is  greater.  Two 
points  may  have  the  same  angular  velocity,  although  the  space 
passed  through  by  each  may  be  very  different.  Thus,  all  the 
points  in  the  pendulum  are  affected  with  an  equal  angular  motion, 
whilst  their  actual  velocities,  or  the  course  traversed  by  each, 
vary  as  the  distance  from  the  centre  of  motion. 

This  description  of  gear  consists  of  a  series  of  projections,  or 
teeth,  regularly  arranged  on  straight,  cylindrical,  or  conical  sur- 
faces, termed  webs,  and  disposed  so  as  to  act  on  each  other,  during 
a  limited  time. 

In  order,  however,  that  the  gearing  action  may  take  place  in  a 
regular,  even  manner,  it  is  indispensably  necessary  that  tho  sur- 
faces of  the  teeth  should  bear  upon  each  other  tangcntially, 
throughout  the  entire  duration  of  their  contact;  and  for  this  pur- 
pose, far  from  being  arbitrarily  designed,  their  form  should  be 
determined  with  the  utmost  geometrical  exactitude,  for  on  their 
form  entirely  depends   their  accurate   and   easy  working.     It  is, 


therefore,  obviously  incumbent  on  the  student  to  give  particular 
attention  to  the  delineation  of  these  teeth. 

The  curves  generally  adopted  in  practice  for  the  outline  of 
teeth,  are  the  involute,  the  cycloid,  and  the  epicycloid. 

It  is  useful  to  investigate  the  nature  and  construction  of  tneso 
curves,  both  on  account  of  then-  application  to  the  teeth  of  wheels, 
and  also  because  of  their  employment  in  several  other  mccnanical 
contrivances. 


INVOLUTE,  CYCLOID,   AND   EPICYCLOID. 

PLATES    XVIII.    AND    XIX. 

I>-\OLUTE. 

Figure     1.— Plate    XVIII. 

197.  When  a  thread  is  unwound  from  the  circumference  of  a 
circle,  and  i3  kept  uniformly  extended,  its  extremity  will  <! 
the  curve  known  as  the  involute. 

This  definition  serves  as  a  basis  for  obtaining  the  geometrical 
delineation  of  the  involute.  Let  a  b  c  ho  the  given  circle  of 
the  radius,  a  o,  and  a  the  extremity  of  a  thread  wound  upon  it. 
Starting  from  the  point,  a,  mark  off,  at  equal  distances  apart, 
several  points,  as  a,  b,  c,  so  near  to  each  other,  that  the  interven- 
ing arcs  may  he  taken  for  straight  lines  without  sensible  error. 
Through  each  of  these  points  draw  tangents  to  the  circle,  or  per- 
pendiculars to  the  corresponding  radii;  and  on  these  tangents  set 
off  distances,  equal  to  the  rectifications  of  the  respective  arcs 
A  b,  A  c,  &c. ;  by  which  means  are  obtained  the  points.  <;',  />'. , ',  &c, 
and  the  curve  passing  through  these  points  is  a  portion  of  the 
involute.  By  continuing  the  development  or  unwinding  of  tho 
thread,  the  curve  may  be  extended  to  a  series  of  convolutions, 
increasing  more  and  more  in  radius,  and  becoming  a  species  of 
spiral.  After  one  complete  evolution  of  the  circumference,  '!"■ 
shortest  distance  between  two  consecutive  convolutions  is  always 
the   same,  and   equal    to  the  development    or  rectification   of    the 


THE    PRACl 


of  -i*-  faaalm  afcast.  wh»b  h 


TU  puiata,  a,  ft,  e,  U-inj  taken  at  equal 
circomfrn  n»,  Ik*    tan.-rnt*   in    r  c,  triple,  Ac, 

thai  of  Ike  first,  A  a  :  and  if.  a*  we  directed,  these  poiota  are  sufli- 
cimtly  Dear  to  <  may  Im  drawn,  with  closely 

approximate  .-  bribing  a  ■uort— ion  of  arcs,  hating 

these  tangent*  for  radii.     Thus,  with  the  point,  a,  aa  centre,  and 
radiaa,  a  a*,  the  fint  arc,  a  a',  is  drawn ;  a:  <  ntre,  b, 

and  radius,  b  ft',  the  aectbd  arc,  m  ft,  in  like  manner;  and  similarly 
with  the  real. 

la  Uk.  Uied  gear, 
.,  wi  sjau  fu,  cams  and  eccentrics. 


.  crt    XV1IL 

196.  9  af  due  is  rolled  upon  a  plane  surface  in  a 

rectilinear  direction,  any  point  in   the   circumference  of  this  dine 
generates  the  nine  called  the  cycloid.     Thus,  any  point  bd 
the  ouUide  of  a  loco:  :i  motion,  describes  as  many 

r  ■  ;  ■  i'  as  the  wheel  make!-  r 

In  order  that 

I  -aary  that  Ike  I  :  take  place  without  . 

.  the  plane;  ii. 

should  be  equal 

I  with,  the  pb 

of  a  circle  of  the   given  radius,  a  o,  and  rolling   upon  a  given 
na,  b  c 
There  arc  several  metl  .-  this  problem. 

.inference,  starting  from  the 

.'lances  equal  to  a  a,  ao  small  that  the  arcs 

.-  1  may  be  taken  as  straight  lines.     Set  off.the  same  <hV 

lance  a  .  snd  at 

• 

r,  which  arc  th  in  the 

. 
on  each  of   which  successively  Mt   off  tl.-  ma  area, 

- .  and  so 
on  tlir  r   o'  c',  paa-M' 

|oirad. 
irve  may  a!».  ■  ' - 

the  original  circle,  and  then  intersecting  these  by  the  area  drawn 

' 

i  wing  area  of  circles  « 
centres,  a»  mdl  .rid  aide  of  flg 

1  icaj,  A  o, 

on  the  horltonlaU,  a-  ..:.<•<•»     equal    I 

r''r  ■' '•   '••'  bet*"  :i  i!..    original  circl<   and  lhi>  f«  rpentli- 

culars  through  tin-  several  i 


thus,  the  distance*,  r  e './/,  p  g>,  »  a  ,  Ac.  are  set  off  from  I  to  a' 

a  to  i ',  3  to  c 

ing  to  .this  last  solution  to  the  left-hand  aids  of  fig.  S,  which  akowa 
n  of  a  aecood  cycloid  similar  to  the  first. 

'.lined,  aa  at  d',  the  poiat  riiirr— pnajdhrg  to 
the  diameter,  A  D.  The  length.  A  c,  of  the  gij  en  aUaigsU  line,  is 
obviously  equal  to  the  rectificalioD  of  the  atstavihiaaafiiumis  of  tho 
generating  circle,  wboae  radius  ia  a  a 

obtained,  having  equal  and  symmetrical  portions  oo  either  aid*  of 

..  al,  c  0,  and  having  for  ita  base  a  line*  double  the  length 

.-cquentJy  equal  to  the  rectification  of  the  enure 

The  cycloid  is  the  curve  more  generally  given  to  the  teeth  of 
w  heel  gear  and  endless  screws. 

EXTEBXAL     IHCTC! 

N    1.— run    XIX. 

dmVfs  from  the  cycloid,  in  that  the 
a  a  straight  fine,  doea 
hieh  is  fixed.     \\ 

an-  in  the  sain-  .'.  taken  generate-,  a  right  or  eylistJri- 

-  are  situate  in  different  planes, 
but  maintaining  a  uniform  angle  to  each  ot) 

butumis  a  tjmrric  ap  ■  rating  circle  m 

auppos.  ntre,  at  the  aame  time  mmng 

the  stationary  < 

►I.  the 
•1  are  analog-     - 
I  o  be  the  radius  of  the  g» :  ■ 
circle,  and  a  c  the  nu! 

a  number  of  equal  pan  1  on  the 

H  as  many  arcs  equal  to  the  a-  r.  staru 

:  A.  as  at  a.  ft,  r.  </.  Ac.     Thr- 
- 
lb*  rad  .-  circle  U ing  genera!- 

-  n  Oation  about  the  stationary 
.  which  are  tl 

- 
:'.  of  the 
:tli    tht-w    p.ints    a- 
.ircs  of  i-jiia!  radii  w  '  rig  circle,  max 

--tiding  arcs,  x  a',  x  V,  x  c',  aa  from 
•e  pa*»ing  tlir 
O*,  ft*.  - 

!      ..'ion. — Tin   p  ■  rmined 

by  >ir:.  r,  area  paasiri. 

in  a',  ft*,  c',  a",  which  are  ao  many  , 
■ 

".  ti  rated  by  tnaaferrmg 

I 
i  its  original  position,  and  the  radii,  c  a,  c  i,  c  L,  passing 


BOOK   OF   INDUSTRIAL   DESIGN. 


through  the  different  points  of  contact  on  the  stationary  circle, 
measured  upon  the  ares  described  with  the  centre,  c,  to  the  same 
ares,  but  so  that  the  extremities  of  the  whole  may  lie  in  the  pro- 
longation of  the  radius,  c  B.  •Thus  the  distances,  ee',ff,gii'  ,&  c, 
are  set  off,  from  1  to  a',  2  to  b',  3  to  c',  &e.  The  diagram  refec- 
ting to  this  construction  forms  the  right-hand  portion  of  fig.  1. 

When  the  generating  circle  lias  made  an  entire  revolution,  the 
euro  obtained  is  an  entire  epicycloid,  a  d  b,  comprising  two  equal 
ind  symmetrica]  portions  on  either  side  of  the  line,  d  e,  which  is 
iqual  to  tlie  diameter  of  the  moving  circle. 

EXTERNAL    EPICYCLOID    DESCRIBED    BT    A    CIRCLE    ROLLING    ABOUT 
A    FIXED    CIRCLE    INSIDE    IT. 

Figure  3. — Plate  XIX. 

200.  For  this  diagram,  which  is  analogous  to  the  preceding  one, 
'  the  radii  of  the  circles  are  given,  c  A  being  that  of  the  fixed  circle, 

and  b  a  that  of  the  moving  one.  Divide  the  first  circle  into  any 
number  of  equal  parts,  in  the  points,  a,  i,  c,  d,  &c,  and  divide  off, 
on  the  larger  circle  of  the  radius,  b  a,  a  like  number  of  arcs,  equal 
to  those  on  the  other  circle,  as  from  a  to  a1,  a'  to  b,  &c.  Then 
with  the  point  c  as  centre,  and  with  the  radius  b  c,  describe  a 
circle, cutting  the  radii,  c  A,  c  a,  c  4,  c  c,  in  the  points,  b,  b',  b2,  b3, 
and  with  each  of  the  last  as  centres,  and  with  the  radius,  A  B, 
describe  arcs,  which  will  be  tangents  to  the  fixed  circle,  at  the 
different  points  of  contact,  a,  b.  c,  in  succession.  Then,  with  the 
centre,  c,  describe  arcs,  passing  successively  through  the  points, 
a',  J',  c',  d',  on  the  moving  circles,  as  in  its  first  position.  These 
last  will  cut  the  arcs  tangential  to  the  given  circle,  in  the  points, 
r2,  b",  c-,  d-,  and  the  curve  passing  through  these  points  is  the 
rpicycloid  sought. 

The  other  two  methods  given,  of  drawing  the  common  epicy- 
cloid, are  also  applicable  \o  this  last  case. 

INTERNAL      EPICYCLOID. 
Figure  2. — Plate  XIX. 

201.  The  epicycloid  is  termed  internal,  when  the  generating 
circle  rolls  along  the  concave  side  of  the  circumference  of  a  fixed 
circle. 

Let  c  A  be  the  radius  of  the  fixed  circle,  and  B  A  that  of  the 
generating  circle.  As  in  preceding  cases,  so  also  here,  we 
commence  by  dividing  the  moving  circle  into  a  certain  number  of 
equal  pails,  and  then  dividing  the  fixed  circle  correspondingly,  so 
that  the  arcs  thus  obtained  in  each  may  be  equal.  We  then  pro- 
ceed as  in  the  ease  of  the  external  epicycloid,  according  to  which- 
ever of  the  three  solutions  we  propose  adopting,  all  being  alike 
applicable.  The  operations  are  fully  indicated  on  fig.  2,  and  the 
same  distinguishing  letters  are  employed  as  in  fig.  1. 

When  the  generating  circle  is  equal  to  half  of  the  fixed  circle, 
the  epicycloid  generated  by  a  point  in  the  circumference  is  a 
straight  line,  equal  to  the  diameter  of  the  fixed  circle.  Thus,  in 
fig.  3,  Plate  XVIII.,  the  epicycloid  generated  by  the  point,  A,  of 
the  moving  circle  of  the  radius,  a  c,  after  a  semi-revolution,  coin- 
cides exactly  with  the  diameter,  a  b. 

If,  with  circles  of  the  same  proportions  as  those  in  fig.  3, 
Pla,te  XVIII.,  we  take  a  point,  D,  outside  the  generating  circle, 
but  preserving  a  constant  distance  from  it,  the  epicycloid  generated 


by  it  will  be  the  ellipse,  D  F  E  G,  having  for  its  transverse  axis  the 
line,  d  e,  equal  to  the  diameter,  a  b,  of  the  fixed  circle,  augment  d 
by  twice  the  distance,  n  a,  of  the  point,  i>,  from  its  extremity;  and 
for  conjugate  axis,  the  line,  g  t,  equal  to  twice  the  same  distance, 

D  A,  alone.  If  it  is  wished  to  determine  this  curve  ace  on 
its  properties  as  an  epicycloid,  and  without  having  recourse  to  the 
methods  given  in  reference  to  Plate  V.,  and  proper  to  the  ellipse, 
it  may  bo  done  by  adding  the  distance,  a  d,  to  that  of  the  radius, 
c  A,  in  each  successive  position  occupied  by  the  generating  circle 
during  its  rotation.  If  the  generating  point  be  taken  inside  the 
moving  circle,  the  curve  produced  will  also  be  an  ellipse. 

The  epicycloid  is  the  curve  most  employed  for  the  form  of 
the  teeth,  whether  of  external  or  internal  spur  or  bevil  wheels. 

Toothed  gearing  may  be  divided  generally  into  two  categories; 
namely,  right,  cylindrical,  or  "spur"  wheels,  and  conical,  angular, 
or  "bevil"  wheels.  In  the  first  are  comprehended  the  action  of  a 
rack  and  pinion,  that  of  a  worm  or  tangent-screw  with  a  worm- 
wheel,  and  finally,  that  of  two  wheels.  We  may  remark,  that  in 
all  these  modes  the  teeth  are  so  formed  and  arranged,  as  to  act 
equally  well  whichever  of  each  couple  he  the  driver,  and  in  which- 
ever direction  the  motion  takes  place. 

THE    DELINEATION    OF    A    RACK    AND    PINION    IN    GEAR. 

Figure  4. — Plats  XVm. 

202.  A  rack  is  a  species  of  straight  and  rigid  rod  or  bar,  formed 
with  teeth  on  one  side,  so  as  to  take  into  or  gear  with  the  teetn  of 
a  right  wheel,  generally  of  small  diameter,  and  in  such  case  termi  1 
a  pinion.     Such  a  rack  is  represented  at  A  E  in  the  figure. 

In  proceeding  to  construct  this  design,  a.s  well  as  for  all  kinds 
of  toothed  gear,  it  is  necessary  to  have  determined   beforehand 
the  thickness,  a  b,  of  the  teeth,  as  this  dimension  varies  accord- 
ing to  the  power  or  strain  to  be  transmitted;  and  rules  and 
for  this  purpose,  will  be  found  at  the  end  of  the  chapter. 

When  the  rack  and  pinion  are  made  of  the  same  metal,  the 
thickness  of  the  teeth  should  be  the  same  in  both.  The  spaces  or 
intervals  between  the  teeth  ought  also  to  be  equal  in  such  case. 
Theoretically  speaking,  the  intervals  should  he  equal  to  the  thick- 
ness of  the  teeth;  but  in  practice,  they  are  made  a  little  v 
admit  of  freer  action. 

203.  The  pilch  of  the  teeth  comprises  the  width  of  n 

and  that  of  the  interval.  In  a  wheel  this  pitch  is  measured  upon 
a  cucle  of  a  given  radius,  termed  the  primitive  or  pitch  circle,  and 
in  the  rack  on  a  straight  line  tangent  to  the  pitch  circle  of  the 
pinion,  and  also  called  the  primilire  or  pitch  line. 

204.  Let  o  c  be  the  radius  of  the  pitch  circle  of  a  pinion  gear- 
ing with  a  rack,  of  which  the  pitch  line  is  a  b.  We  propose,  in 
the  first  place,  to  determine  the  curve  of  the  teeth  of  the  pinion, 
so  as  to  gear  with  and  drivo  the  rack,  and  we  shall  subse  |uentiy 
determine  the  curve  of  the  teeth  of  the  rack,  enabling  it  to  gear 
with  and  drive  the  pinion. 

The  operations  consist  in  rolling  the  straight  line,  a  c,  tangen- 
tially  to  the  pitch  circle,  O  c;  during  this  mo-vement,  the  point,  c. 
will  generate  an  involute,  c  D,  which  may  be  drawn  in  the  manner 
indicated  in  fig.  1 — a  construction  Which  is  further  repeated  at 
a'  ,1'.  on  one  of  the  teeth  of  the  pinion,  fig.  4. 

This  curve  possesses  this   property,  that  if  the  teeth  are  formed 


la  it.  and  the  pinion  b>  turn. 

wiB  alwayt  be  in  the  strai;rhl  line.  a.  b,  tra 

(Batty  the  aatn. 

r.  ntrr,  that  k  at  th» 

pilrh  rin-le  mi:..  s«  many  e<]aal  part* 

intma  - 

• 

fted  U  ■  vh  line,  a  b,  of  the  rack,  an  many  times  as 

trically 

indicated  at  o  if,  no  that  the  pinion  may  ■ 

they  may 

■ 

■ 

- 

I  B. 

■ 

tooth,  II,  <>("  the 
rack,  should  continue  to  impel  it  nnl         * 

.... 

all  th.   '  :re. 

To  a  rtino  of  tin   ' 

'.its,  bf, 
ne,  a  n,  nnil  | 
■ 

«.  at  the  same  time,  f..rm  tbj 

.lit  line,  m  ».  I 

Ih  nf  the 

the  t. ••■th  with 
iriUv,  which,    ai 

h  cima, 
tln  in  to  ilri\. 

i  k  at  it-  pitch  i 

■  • 

- 


Lh  nf  the  rail.  ■    and  to 

then  !«•  in  th- 
linn,  if  Iron  th..  i>. -int.  L,  tl 

. 

tat,  l.    If,  tl 

• 

]iitch  line  of  the  rack,  as  was  aln:i. 
]4niim. 
To  ffa 

c  '<*,  ami  through  tl  • 

i  line,  m  !c,  parallel  to  a  r..     I 

■ 
i  j.  k  I,  &«•.,  which  an 

- 
. 
.  nd  the  side*  of  the   ' 
joined   ' 

ribod  with  a  n  uu  Uiat 

lad  drawn. 
■  would  be  a  ti 
dotatnfaimg  tin-  runes  in  lb  th,  it  i* 

.-•I  ..r  tliiu  h  o 
n  nr  template,  by  the 

. 
- 
• 

uith,  ami,  in   i  ir  arc  is 

i  radius 

With  thin 

view  the  are  should   b  the  tooth,  sn.l 

I 
'i   an-   f.r  tin-  tnie  . 

nee  this  arc  I 
point,  r,  l  iual  to 

I.  q,  ami  to  be  a  tan, 
o  r,  an! 

. 

ij  afterwards  i- 


BOOK  OF  INDUSTRIAL  DESIGN. 


with  the  same  radius,  care  being  taken  to  keep  the  centres  in  the 
line,  a  b. 

An  analogous  operation  will  give  the  proportions  of  the  are, 
substituting  the  curve  of  the  pinion  teeth. 

THE    GEARING    OF    A   WORM   WITH   A   WORM-WHEEL. 
Figures  5  and  6. — Plate  XVIII. 

207.  This  system  of  gear  is  constructed  on  tho  same  principles 
as  that  of  a  rack  and  pinion,  which  method  requires  that,  in  the 
first  place,  the  worm  and  worm-wheel  be  supposed  to  be  sectioned 
by  a  plane  passing  through  tho  axis  of  the  former,  and  at  right 
angles  to  that  of  the  latter.  The  representation  of  this  section 
becomes  analogous  to  the  diagram,  tig.  4 ;  that  is  to  say,  tho  pitch 
circle,  g  c  j,  of  the  worm-wheel  being  given,  and  also  the  straight 
pitch  line,  A  B,  of  the  worm  tangential  to  this  circle,  and  parallel 
to  the  axis  of  the  worm,  the  involute  curve,  c  D,  is  sought  for  the 
teeth  of  the  wheel,  and  the  cycloid,  c  k,  for  those  of  the  worm. 
The  lengths  of  these  curves  are  limited,  as  in  the  preceding  exam- 
ple, and  when  the  whole  is  complete,  an  outline  will  be  produced 
similar  to  the  tinted  portions  of  fig.  6.  It  is  in  this  manner  that 
the  gearing  of  the  worm  and  worm-wheel  is  made  to  depend  upon 
the  same  principles  as  that  of  a  rack  and  pinion,  and  the  same 
method  may  be  employed  in  construction  in  determining  the  outline 
of  the  teeth,  as  we  have  shown. 

To  represent  the  worm  and  worm-wheel  geometrically  in  exter- 
nal elevation,  instead  of  a  section  of  the  teeth  alone,  it  is  necessary 
to  know  the  diameter  and  pitch  of  the  worm  on  the  one  hand,  and 
the  thickness  of  the  worm-wheel,  fig.  5,  on  the  other. 

Let  iu'  a'  be  the  distance  of  the  pitch  line,  a  b,  from  the  axis, 
M'  n,  of  the  worm,  and  a  b  the  width  of  the  wheel.  When  the 
worm  is  single-threaded  (177),  the  pitch  of  the  helix  is  the  same 
as  that  of  the  teeth,  and,  therefore,  the  thickness  of  a  tooth,  added 
to  the  width  of  an  interval.  In  this  case,  each  revolution  of  the 
worm  turns  the  wheel  to  the  extent  of  one  tooth,  and  this  is  the 
arrangement  represented  in  the  figures.  If  the  worm,  however, 
is  double  or  triple-threaded,  its  helical  pitch  will  bo  correspond- 
ingly two  or  three  times  the  pitch  of  the  teeth;  and  in  such  case, 
each  revolution  will  turn  the  wheel  to  the  extent  of  two  or  three 
teeth. 

The  worm-wheel  being  of  a  certain  thickness,  and  requiring  to 
gear  with  the  convolutions  of  the  worm,  must  necessarily  have  its 
teeth  inclined  to  correspond  with  the  obliquity  of  the  worm-thread. 
It  is  _  further  to  be  observed,  that  the  sides  of  the  wheel-teeth 
being  simply  tangential  to  the  worm-thread,  contact  cannot, 
rigorously  speaking,  take  place  in  more  than  one  point  of  each 
tooth  and  convolution.  This  point  constantly  changes  with  the 
motion,  but  always  lies  in  the  plane,  o'  m',  of  the  section. 

In  delineating  the  convolutions  of  the  worm-thread,  helices 
have  to  be  drawn  passing  through  the  external  corners,  d,  e,  and 
internal  corners, /,  g.  We  have  repeated  these  points  to  the  left- 
hand  side  of  fig.  6,  where  the  required  operations  are  fully  indi- 
cated, in  connection  with  the  projection,  fig.  5,  and  in  accordance 
with  the  principles  already  explained  (173).  The  corresponding 
points  in  the  two  figs.  (5  and  6)  are  distinguished  by  the  same 
letters  and  numbers. 


208.  For  the  representation,  in  external  elevation,  of  the  teeth 
of  tho  worm-wheel,  it  is  required  to  develop  a  portion  of  the 
cylindrical  surface  generated  by  the  revolution  of  the  pitch-line, 

A  B,  about  the  axis  of  the  worm,  and  containing  the  portion, 
A.iklm,  for  example,  of  the  helix,  described  by  the  central  point 
of  contact,  A.  To  obtain  this,  make  the  line,  e'  a',  fig.  7,  equal  to 
the  semi-circumference,  a'  m  e2,  rectified.  At  the  point,  e',  erect 
the  perpendicular,  c'  e',  and  make  it  equal  to  c  e,  fig.  G,  or  half 
tho  pitch,  and  join  e'  a',  whereby  will  be  obtained  the  actual 
inclination  of  the  worm-thread.  On  each  side  of  the  point,  m,  on 
e'  a',  mark  distances,  m  a'  and  m  b',  equal  to  mf  a  and  m  b,  tig.  5, 
and  through  these  points  draw  parallels  to  c'  e',  and  tie  portion, 
p  q,  of  the  enclosed  line  comprised  within  them,  will  serve  to  deter- 
mine the  width  and  inclination  of  the  teeth  of  the  worm-wheel. 
Through  tho  points,  ;>,  r,  draw  p  t  and  r  s  parallel  to  e'  a',  arid 
mark  otl*  the  distances,  I  s  and  s  q,  which  are  equal,  on  the  pitch 
circle  of  the  wheel,  fig.  6,  from  s  to  t  and  q,  after  having  drawn 
through  the  points,  s,  but  only  in  faint  pencil  or  dotted  lines,  tho 
contours  of  the  teeth  as  sectioned  at  f  and  g'.  It  is  then  sufficient 
to  repeat  theso  outlines  through  the  points,  t  and  q,  limiting  their 
length  by  the  same  internal  and  external  circles. 

Finally,  the  edge  view  of  the  worm-wheel,  fig.  5,.  being  the 
lateral  projection  of  the  teeth,  is  determined  by  squaring  across  the 
points,  u,  v,  x,  to  «',  t>\  xl,  which  give  the  interiors  of  the  teeth  : 
and  the  points,  u-,  v",  x",  being  squared  over  to  u3,  v3,  x3,  give  tin  ir 
exterior  edges. 

Worm-wheels  are  sometimes  constructed  with  the  form  of  the 
teeth  concave,  and  concentric  with  the  axis  of  the  worm,  with  the 
view  of  their  being  in  contact  with  the  convolutions  ol  the  worm- 
thread  throughout  a  certain  extent,  in  place  of  onJIJ  Couching  at 
single  points. 

This  arrangement,  which  requires  a  particular  operation  for  its 
construction,  is  generally  adopted  when  great  precision  is  required, 
and  when  it  is  wished  to  avoid,  as  much  as  possible,  any  play 
betw-een  the  teeth  and  the  worm-thread  during  the  transmission  "I' 
motion. 


CYLINDRICAL  OR  SPUR  GEARING. 

PLATE    XIX. 
THE    EXTERNAL    DELINEATION   OF   TWO  SFUR-WHEELS    IN   GKak. 

Figure  4. 
209.  Spur-toothed  wheels  are  such  as  have  their  teeth  parallel, 
and  lying  upon  a  cylindrical  surface  or  web.  When  a  couple  of 
such  wheels  are  of  unequal  size,  the  smaller  one  is  generally 
called  a  pinion,  and  the  larger  one  a  Bpur-whee).  Two  wheels, 
which  are  intended  to  gear  together,  cannot  work  satisfactorily  in 
concert,  unless  their  radii  or  pitch  circles  are  exactly  proportional 

to  the  number  of  teeth  contained  by  each.  Consequently,  in 
order  to  construct  designs  for  couples  of  toothed  wheels,  it  i» 
necessary  to  know — tho  number  of  teeth  of  each,  and  the  radian 
of  one  or  other  of  then  ;  or  the  radii  or  diameters  of  both,  and  the 
number  of  teeth  of  one;  or  the  distance  between  their  centres,  and 
the  radius  or  number  of  teeth  of  one;  or  finally,  the  number  <>i 
revolutions  of  each  in   the  same  time,  and  the  distance  between 


tSrir  eeatrea.  or  lb*  radios  and  numU-r  of  teeth  ofoMof  thesn. 
la  lb*  rules  and  data  at  the  rod  .  •  f  t  hi.  chapter,  will  be  found  the 
.1.  :  ii.   ..  >.  al  problems  involved  in  tbcee  various  cases. 

lowing  data,   I  -=  400, 

dm*  bring  tba  isapeetive  radfl  "f  '" 
.    the  number  af 
.•Main  Ibe  nnmbrr  of  .  by  tbo 

ag  proportions!  furmuU : — 

'.  m  40. 
Then  describe  the  pitch  circlca  of  the  radii,  A  a  and  *  c,  and 

■btaining  the  pitch,  or  the  central  point  of  each  I 
•  c  name  on  b 

i  e<)nal  porta,  i  -■  and,  at 

the  sai 

l  c,aa  a 
'   o,  and 
roll   round   t. 

.   in  rafcranea  t"  li^'.  1 ;  and 

■ 

•lla^nun.      It 

mil  round  the 
. 

b  o,  as 
!  a  por- 

'urniny 
| 

.il  tune 

I 

j 

r  ra.lhv 


■ 
is  intended  alw.. 

..c  teeth  of  the  spur-wheel  would  only  require  to  be 

'  J,  and  those  of  the  pinion,  like  the  portion  of 

•  1  for  the  naif  ..f  distinction  ;  but  generally, 

-  reasons,  all  epur  gear  is  ao  cooatructed  ■ 

ally,  and  equally  well,  whichever  be  the  driver,  and  we 

',h  of  the  pinion,  so  tint  it  may,  in 

-  rf.irm  that  fui 

i ;«  a  circle  with  the  centre,  &,  of  the  radium 

a  i ,  taken  aa  a  diameter ;  and  suppose  that  circle  to  n.ll  round  the 

i    point,  a,  at  present  in  cob. 

tact,  will  generate  the  epicycloid,  a  u  which  is  the  propai  curve 

to  be  .  i ■ ..  con- 

. 
the  name  manner  round  (he 
i   B  D,  and  tl>  - 

>  in   the  aame 

: 

..rv,  b/*,  equal  I 

scribed  with  tl 
iuit  >h"rt  n|   '  .J  circle 

paaaage,  as  air. 

cat,  and 

similar    I 

In  !L< 

-  Dcceaaary  ft  ;. 

. 
: 
g.  "hi.  h  alalia, 

\*ar. 

■ 
- 


BOOK  OF  INDUSTRIAL  DESIGN. 


same  operations,  modified  to  suit  the  different  positions  of  the 
parts  with  respect  to  each  other.  Thus  the  curve,  B  I.,  of  the 
pinion  tooth,  is  generated  by  the  rolling  round  the  pitch  circle, 
G  b  H,  of  the  circle  described  with  the  centre,  o,  and  radius,  o  B, 
equal  to  the  half  of  b  c,  the  radius  of  the  pitch  circle,  d  b  e,  of  the 
larger  wheel.  Tills  is  an  application  of  the  operations  explained 
in  reference  to  fig.  3.  The  flanks,  B  a,  or  the  sides  of  the  teeth, 
are  obtained  by  simply  drawing  radii,  or  lines  converging  in  the 
point,  e. 

In  the  same  manner,  the  curve,  b  f,  of  the  teeth  of  the  large 
wheel,  is  generated  by  rolling  along  the  interior  of  its  pitch  circle, 
b  d  e,  a  circle  described  from  the  centre,  o',  and  radius,  B  o',  equal 
to  half  the  radius,  B  A,  of  the  pitch  circle,  G  B  H,  of  the  pinion. 
These  curves  being  obtained,  the  outlines  of  the  teeth  are  com- 
pleted in  the  manlier  explained  in  reference  to  fig.  4.  It  may, 
however,  be  observed  that,  in  the  diagram,  fig.  5,  though  the  teeth 
might  be  cut  off  by  a  circle  passing  through  the  point,  /  and 
described  with  the  centre,  a,  they  are  prolonged  beyond  that,  so 
that  the  teeth  remain  longer  in  contact,  and  a  greater  number  of 
teeth  are,  consequently,  engaged  at  one  time,  allowing  the  strain 
to  be  distributed  over  a  greater  number  of  points.  It  is  the  fact 
of  the  curvatures  of  the  two  lines  of.  teeth  being  in  the  same  direc- 
tion, which  admits  of  a  greater  number  of  teeth  being  engaged  at 
once,  without  that  increase  of  friction,  and  other  disadvantages, 
which  would  result  from  such  an  arrangement  with  wheels  like 
fig.  4. 

THE    PRACTICAL   DELINEATION   OF   A   COUPLE    OF   SFUK-WHEELS. 
Plate    XX. 

213.  In  the  cases  treated  of  in  the  preceding  sections,  which 
comprehend  the  general  principles  involved  in  rack  and  wheel 
gearing,  we  have  assumed  that  the  rack  and  pinion,  or  pinion  and 
spur-wheel,  are  constructed  of  the  same  material,  and  in  this  case 
the  thickness  of  the  teeth  is  the  same  in  any  two  working  together. 
It  very  often  happens,  however,  in  actual  construction,  that  one 
of  the,two  has  wooden,  and  the  other  cast-iron  teeth,  or  of  other 
dissimilar  material.  When  this  is  the  case,  the  thickness  of  the 
one  description  must  necessarily  be  greater  than  that  of  the  other, 
to  compensate  for  the  difference  in, the  strength  of  the  materials. 
The  pitch,  however,  will  still  be  the  same  for  both  wheels;  for, 
since  the  intervals  on  one  wheel  correspond  to  the  teeth  on  the 
other,  a  tooth  and  an  interval  on  one  must  obviously  be  equal  to 
an  interval  and  a  tooth  on  the  other.  A  couple  of  wheels  of  this 
description  are  represented  in  plan  and  elevation,  in  figs.  1  and  '2. 

We  here  assume  the  wheels  to  be  in  the  ratio  to  one  another  of 
3:4;  whence,  giving  the  pinion  36  teeth,  the  spur-wheel  must 
have  48.  After  dividing  the  pitch  circle  of  the  spur-wheel,  drawn 
with  the  radius,  c  b,  into  96  equal  parts,  the  points  of  division 
representing  the  centres  of  the  teeth  and  of  the  intervals,  and  the 
pitch  circle  of  the  pinion  drawn  with  the  radius,  a  b,  likewise,  into 
72  equal  parts — with  the  centres,  o  and  o',  describe  the  circles 
•  wii'ch  generate  the  epicyeloidal  curves,  e  f  and  B  l.  Take  4y  of 
the  pitch,  b  c,  for  the  thickness  of  the  wooden  tooth,  d  e,  and  ,'T 
for  that  of  the  cast-iron  tooth,  allowing  the  remaining  Jy  for  the 
play  in   working.     Next  draw  a  series  of  radii,  to  indicate   the 


Hanks  of  the  teeth,  both  of  the  pinion  and  spur-wheel,  and  at  the 
point  of  their  junction  with  the  pitch  circle,  draw  the  curved  por- 
tion of  each,  with  the  aid  of  a  small  pattern  or  template,  cut  to 
the  curves,  n  l  and  c  f;  and,  finally,  limit  the  lengths  of  the  teeth 
and  the  depths  of  the  hollows  in  the  manner  already  pointed  out, 
in  reference  to  Plate  XIX. 

As  draughtsmen  are  generally  satisfied  with  representing  the 
epicyeloidal  curves  by  area  of  circles  which  almost  coincide  with 
them,  and  nearly  fulfil  the  same  conditions,  such  arcs  imi-l  he 
tangential  to  the  radial  sides  of  the  teeth  at  their  points  of  inter- 
section with  the  pitch  circle.  They  are  determined  in  the  follow- 
ing manner: — Let  fig.  10  represent  one  of  the  pinion  teeth,  drawn 
to  a  larger  scale.  Through  the  point  of  contact,  b,  draw*  a  tan- 
gent, B  o,  to  the  pitch  circle;  then  bisect  the  chord,  !i  n,  which 
passes  through  the  extremities  of  the  curve,  by  a  perpendicular, 
which  will  cut  the  tangent,  B  o,  in  the  point,  v.  This  is  the  centre 
of  the  arc,  b  m  n,  which  very  nearly  coincides  with  the  epicj  - 
curve.  The  same  arc  is  repeated  for  each  side  of  all  the  teeth  "f 
the  pinion,  the  radius,  b  o,  being  preserved  throughout.  An 
analogous  operation  determines  the  radius  of  the  arc  to  be  suliMi- 
tuted  for  the  curve  in  the  teeth  of  the  spur-wheel. 

It  is  generally  advisable  to  make  wooden  teeth  about  three- 
fourths  as  long  as  the  pitch,  and  east-iron  teeth  about  two-thirds 
as  long.  In  no  case,  however,  should  the  lengths  of  the  teeth  in 
the  two  wheels  geared  together  be  less  than  those  obtained  by 
calculation,  and  determined  by  the  points,/,/1,  situated  on  the 
circles  described  with  the  centres,  o,  o',  by  which  the  epicycloids 
are  generated.  The  ratio  of  the  curved  external  portion,  "  m,  of 
the  tooth  to  the  flank,  n  p,  is  4:5.  In  other  words,  the  whole 
height  or  length  of  the  tooth  bi-in lT  divided  into  '.'  equal  parts,  4  of 
these  are  to  be  taken  for  the  length  of  the  curved  portion,  and  5 
for  the  rectilinear  flanks.  When  the  teeth  are  of  cast-iron,  the 
thickness,  p  q,  of  the  web  should  be  equal  to  the  thickness,  r  s,  of 
the  tooth.  Sometimes  it  is  made  only  ,'ths  of  this;  but  in  that 
case  it  is  strengthened  by  a  feather  on  the  interior. 

For  wooden-toothed  wheels,  since  it  is  necessary  that  the  tenon, 
t,  of  the  tooth  be  firmly  secured,  the  web  is  made  of  a  thickness, 
p  q,  often  double  that  of  the  tooth.  The  tenons  of  the  teeth  must 
be  adjusted  very  carefully  and  accurately  in  the  web.  They  are 
made  with  a  slight  taper,  and  are  secured  on  the  interior  of  the 
wch  either  by  iron  pegs,  as  at  u,  passing  through  them,  or  bj  a 
series  of  wooden  keys  or  wedges,  r,  driven  in  between  tin 
forming  strong  dove-tail  joints.  These  two  methods  of  fixing  the 
teeth  are  shown  at  different  parts  on  fig.  1.  and  more  in  detail  in 
fig.  7.  There  is  a  third  modification,  which  also  possesses  some 
advantages.  We  have  represented  it  at  T,  fig.  3,  whence  it  will 
he  seen  that  it  consists  in  forming  the  teeth  with  a  couple  of 
shoulders,  :.  which  allow  of  the  tenons.  I,  being  made  much 
stronger, and  also  take  away  thereby  some  of  the  weight  of  metal, 
two  objects  of  great  importance. 

The  width,  x  y,  of  the  teoth  is  equal  to  two  or  three  times  their 
pitch.  In  wheels  entirely  of  cast-iron,  the  web  is  of  the  same 
width  as  the  teeth:  but  it  is  much  broader  when  the  teeth  a  y  of 
wood,  for  it  requires  to  be  mortised,  to  receive  the  tenons  of  the 
teeth,  and  should  have  a  width  equal  to  that  of  the  teeth,  plus  an 
amount  equal  to  once  and  a  half  or  twice  their  thickness.     We 


•    in  »Wb    of    moderate    - 
the  boat,  r\  by  arm*,  v.     The  t. 
tb**e  inn  vai 

In  the  preaeot  raae  uV  vanna;  thia  tp. 

other    uaaiina.  being   more    particu'.. 
number  of  !•«  :h  are  d  'list  the 

concave  quarter -round  moul. 

cated  in  fitf*.  5  and  6,  which  rcorc- 

-  are  united  :  ■',(•  inn 

! 

•till,  an 

feathers  being  united,  M  it  were,  to  the  body  uf  tin-  ami  without 
any  additions; 
In  all  caar*. 

radnally 

.  rdly . 

'.•■,  3 — 1 — .">.  00   fig.  I.      W 

-.  that  at  the  upper  part  of  • 
I*  parallel  t«i  tli«-  arm, or  (be  ami  it, 

■■r  a  a', 

mat  it  may  I*-  projected  in  d  a  whh- 

the  am-  as  in  the  ob  nted  in 

In  ll 

■ 


THE  DELINEATION  AND  CONSTRUCTION  OF  WOODEN 
PATTERNS  FOB  TOOTHED  WHEELS 

1'I.ATK    XXI. 

•want  iai  i 

mon  the 
•  ii  pai- 

•h.n  .if  the  |. 

■   of  ill.- 

|*rta — an  that 

mat  make  allowance,  nut  only  (or  lb 

away  l.y  turning  and  finishing  afterward*.      M 

I  Zeroed  with  a 


I   difficult — «m.. 

actual  luam  • 

mind  tin  ~-  various  c  -n-M.  rati  on*,  we  may  proceed 

'«.  »u  Ii  aa  are 
\  \ 

r*TTXJi«  oi 

cipal  pii 

I  ;ort»  in  succ<  -- 

- 
in  thiil. 

built  u|i  like  brickwork,  the 

r. 
quite  dry.  is  put  into  a   lathe,  ami   there   i 

|  arallcl,  and  tie 
detenu  .mi  upon    a 

ai-tual    -  a 

At  t!. 

or  naDed  on.     i 

BOM, 

Tin'  l>oi«  i-  i  , 

.  I  when  the  «' 

;  .irati  ly  to    ti'. 

ncaa  oi  '■!'  the  arm. 

lu  of  a 

I 
of  that   part  of  the  arm  which  i»  afterward*  the  only  part 


BOOK  OP  INDUSTRIAL  DESIGN. 


in  the  casting,  but  also  comprising,  above  and  beyond  this,  the 
projections  by  which,  in  the  pattern,  it  is  attached  to  the  boss  on 
the  one  hand,  and  to  the  crown  on  the  other.  The  extremity,  a, 
of  the  boss  end  of  the  arm  is  in  the  form  of  a  sector,  correspond- 
ing to  a  sixth  part  of  the  circle  of  the  boss,  the  pinion  having  six 
arms;  the  lateral  facets,  /),  of  this  part  are  grooved  out,  to  receive 
small  tongue-pieces,  or  keys,  c,  fig.  1,  so  as  to  form  a  strong  joint 
when  glued  together.  The  other  extremity,  d,  of  the  arm  is  cut 
circularly,  to  the  form  of  the  crown,  or  web,  into  which  it  is  fitted, 
penetrating  to  a  slight  extent,  tho  crown  being  previously  formed 
with  a  socket  to  receive  it. 

Next,  the  feathers  have  to  be  attached  to  the  body,  c,  of  the 
arm.  These  feathers,  B,  are  each  cut  out  in  separate  pieces,  to  . 
(he  shape  indicated  in  fig.  5 :  they  have  supplementary  projec- 
tions, e  and  f,  at  their  opposite  extremities,  whereby  they  are  fixed 
into  the  crown  and  boss.  When  all  these  feathers  are  in  their 
place,  and  the  arms  glued  into  the  crown,  the  two  portions,  D,  d, 
of  the  boss  are  fixed  to  them,  the  grooves  for  the  reception  of  the 
ends  of  the  feathers  being  glued,  as  well  as  the  other  parts,  to 
give  greater  solidity.  Finally,  the  boss  is  surmounted  by  the 
conical  projecting  pieces,  f,  f,  which  serve  to  produce  in  the  mould 
the  cavities,  or  sockets,  which  retain  the  loam  core  in  position,  the 
core  being  provided  to  produce  the  eye  of  the  wheel,  into  which 
the  shaft  is  fitted. 

To  give  compactness  and  strength  to  the  whole,  a  bolt,  G,  is 
passed  through  the  centre;  and  this  method  of  securing  permits 
of  the  core  projections,  f,  f,  being  changed  for  larger  or  smaller 
ones,  if  desired,  without  having  to  pull  the  entire  wheel  to  pieces. 
If,  to  add  to  the  elegance  of  the  shape  of  the  wheel,  it  is  wished  to 
ornament  the  arms  with  mouldings,  as  at  i,  these  are  applied  at 
the  angles  of  junction  of  the  feathers  with  the  body  of  the  arm. 
These  are  simply  glued  or  nailed  on.  The  sectional  view,  fig.  6, 
shows  the  form  and  position  of  these  mouldings. 

It  is  to  be  observed  that,  in  wheels  of  a  moderate  size,  when 
oast-iron  teeth  are  to  work  on  casHron,  they  are  at  once  cast  to 
the  exact  shape,  and  the  pattern  is  constructed  accordingly  ;  but 
it  is  almost  always  indispensable,  where  cast-iron  and  wooden 
teeth  have  to  work  together,  to  finish  and  reduce  the  former  after 
being  cast ;  and  the  projections,  B,  on  the  pattern  answering  to 
them,  must  consequently  be  made  of  larger  proportions  every  way, 
to  provide  for  the  quantity  of  metal  taken  away  in  the  finishing 
process. 

PATTERN   OF   THE    WOODEN-TOOTHED    STOR-WHEEL. 

216.  Figs.  7,  8,  and  9  represent,  in  elevation,  plan,  and  vertical 
section,  the  wooden  pattern  of  the  spur-wheel,  which  gears  with 
the  pinion  just  described.  It  consists,  like  that  wheel,  of  the 
crown  or  web,  the  boss,  and  the  arms  ;  and  these  various  parts, 
which  are  designated  by  letters  corresponding  to  those  employed 
in  the  preceding  example,  are  constructed  exactly  in  the  same 
manner. 

There  is,  however,  an  essential  difference  in  the  exterior  of  the 
crown :  in  place  of  this  carrying  the  projections,  B,  cut  to  the 
shape  of  the  teeth,  and  such  as  will  actually  be  produced  on  the 
casting,  it  has  other  projections,  b',  of  a  simpler  form,  intended  to 
produce  in  the  mould  the   sockets  for  receiving  the  core-pieces 


which  form  the  mortises  in  the  casting,  to  receive  the  tenons  of 
the  wooden  teeth.  These  projections  are  let  into  the  crown,  or 
simply  applied  thereto,  and  fixed  by  nails,  as  at  /.  or  by  screws,  as 

at  m,  the  latter  method  being  preferable,  as  it  has  the  advantago 

of  permitting  the  number  of  teeth  to  be  changed  without  injury  to 
themselves  or  to  the  crown.  In  the  Wooden  pattern,  the  length 
of  the  projections,  B',  is  carried  to  the  edge  of  the  face  of  the 
crown,  on  that  side  which  descends  into  the  lower  half  of  the 
mould-frame,  to  allow  of  the  more  accurate  adjustment  of  the  coro- 
pieces,  and  also  to  facilitate  the  recovery  of  the  pattern  from  the 
mould.  These  core-pieces,  however,  are  so  formed  as  to  make  the 
mortises  no  wider  than  is  necessary,  and  to  leave  a  sufficient  thick- 
ness of  metal  for  the  strength  of  the  crown,  as  already  pointed  out 
in  reference  to  Plato  XX. 

CORE-MOULDS. 

217.  The  core-pieces  for  the  mortises  should  not  only  he  placed 
at  equal  distances  apart  throughout  the  circumference  of  the  crown, 
but  they  must  all  also  be  of  precisely  the  same  form  and  dimen- 
sions throughout,  so  that  the  mortises  may  he  perfectly  equal. 
With  this  view,  a  wooden  core-box  or  mould  is  made  ;  and  there 
are  several  methods  of  doing  this.  Thus,  fig.  10  represents  a  thro 
view,  and  fig.  11  a  horizontal  section,  through  the  line  3 — 1  in 
fig.  10,  of  one  form  of  core-mould,  consisting  of  a  single  piece.  Tho 
portion,  n,  of  the  cavity  corresponds  to  the  projecting  core-piece, 
b',  outside  the  crown,  and  the  portion  marked  n,v  tho  mortise,  or 
hollow  socket,  in  the  crown  :  this  last  has  the  same  section  as  the 
crown  in  the  width  of  the  cut-out  part.  The  moulder  fills  tho 
cavity  of  the  core-mould  with  loam,  previously  prepared,  and  after 
pressing  it  well  in,  levels  it  oft' with  a  straight-edged  doctor  or 
scraper;  he  finally  inverts  the  mould,  thus  releasing  the  core  com- 
plete. The  operation  is  repeated  as  many  times  as  there  are  teeth  ; 
and  when  the  cores  are  all  dry.  they  are  placed  with  "Teat  care  in 
the  mould,  their  supplementary  projections,  b',  being  let  into  the 
sockets  formed  to  receive  them— thereby  insuring  the  accuracy  of 
their  adjustment. 

Fios.  12,  13,  and  14,  show  another  construction  of  wooden  core- 
mould,  formed  in  two  separate  pieces,  h  and  i.  These  have  be- 
tween them  the  cavity,  n  o,  corresponding  to  that  in  the  one  just 
described.  In  this  last  case,  the  surface  of  the  core  which  re- 
quires to  be  levelled  oft"  with  a  scraper,  is  only  at  one  of  the  extre- 
mities instead  of  on  the  lateral  faces,  as  in  the  other,  and  the  eon  -> 
are  released  by  separating  the  two  pieces,  n,  i.  which  are  render!  I 
capable  of  accurate  adjustment  to  each  other  by  means  of  marking. 
pins,  k. 

To  return  to  the  wheel  itself:  when  it  is  of  very  large  dimen- 
sions, the  blocks,  P,  of  the  boss  are  secured  together  by  two  or 
more  bolts,  c;,  in  place  of  one. 

The  mould  for  the  wheel  is  in  two  pieces,  the  lower  frame,  or 
"drag,"  being  let  into  the  ground  in  the  moulding  shop;  the  upper 
frame  or  top  part,  is  moveable,  and  it  will  be  obvious  that  very 
great  care  is  required  to  lift  this  oil' the  pattern,  so  as  not  to  injure 
the  regularity  and  sharpness  of  the  impression;  and  for  this  pur- 
pose, sufficient  "draw"  or  taper  must  he  given  to  the  various  parts, 
as  the  crown,  the  boss,  and  the  feathers  on  the  arms,  as  already 
pointed  out. 


' 


two   arrvw-atii; 

or  bnua,  «ro  countersunk  into 

>,Tnmis  and  to 
■ 

:   plana,  made   fur  ui'tual 

■ 


.:>  PI  VCT1CAL  DATA. 

IHISG. 

i  fundamental  rale,  thai 

r   luii-t 

tofl 

• 
It  follows  from  ilii-  a  the  radii  of 

tha  ii iimlxr  of  !<i Hi  of  one  of 
In  r,  and  reciprocally. 
al  tin-  Dumber  of  teeth  of  a  wheel  of 
U)o  nuliu-s  R  ;  and  n  :  ■    Dumber  "l  ii .  lli  of  :i  wheel 

of  the  ■  re  me  direct  proportionals,  i  :  n  ::  ■  :  r; 

i,  alany  time,  ascertain  anyone  of  the  terms  when 
■vn.    . 
/  .■!«•  "I"  :i  s|.ur- 

.  i  the  Dumber  of  teeth  on  ii  76,  what  should 
■  h  "ii  a  pinion  gearing  with  it, 

_ 

: :  19  :  9  .  whence 

75  x  8 


ia 


lively,  be  the  somber 
of  the  teeth  •  ■!"  a  ■par-wheel  and  pinion,  and  19  inches  th 
«>f  the  pitch  circle  «f  the  Former,  the  mdma  of  the  piteh  • 
•Ji«  latu-r  maj  be  found  by  meana  of  the  proportion — 
70 :  SO  ::  i-  :  r;  whence, 

W  x  12       o.     , 
r  =  — — —  =  8  n 
76 

ii  the  Dnmbera  of  revolutions 

ir-wheel  and  pinlbn  in  gear  with  each  other, 

are  In  U  -.  radii,  or  nnn> 

I 

1  .  ■  ni  tl»-  velocity  of  rol 

■  which  eqnala  r, 

and  the  nomber  of  the  teeth  n,  and  patting  i  the  relo- 

il  whieh  the  pitch  drela  radk 

R  .11! 

V  :  ,  ::  r:  R, 
and 

V  :  i   : 

1  ramie,  as  hi  the  format 

when  the  tlir>-<-  others  are  known. 


I  I  \  |    ulii.-h 

- 
a  lth  il,  and  i 

D 


. 


I  circle  radius  of  the  pinion. 

a  a  pinion  at  the  riIo 
tinute,  uliat  hlinul.i  he  the  nomber 
of  the 

:  n  ; 

■ 


78 


=  20, 


thr  namber  of  teeth  the  pinion  mast  ; 

ii  oom- 
mnnieation  with  one  another  by  eordi 

s i  known 

is  the  distance  apart  of  their  centres,  the  namber  of  teeth  which 
ry,  orthe nber  of  their  revolutions  In  Ii 

time.      In  Ilii-  • 

ili.-  .—mil  of  their  revolutions, 
nnd  between  their  r<  ■  and  revolutions;  and,  on  the 

other  hand*  a  direct  proportion  between  the  i 
the  —  < j it i  of  tin-  teeth  on  I •. . t Ii  whoels,  radii,  oi 

tin-  nomber  of  teeth  ol 

■  ■  apart  u|"  lli. 

pinion  of  the  respective  radii,  K.  r,  and  Dumber  of  teeth,  v 

\  t  the  following 

inverse  proportion, 

D:  V  +  t::R:  V; 

Ii  :  N    -    -  ::  N  :  It. 
/      •   /  Lot  40  inches  l«-  tha  distsne*  between  iii» 

.  »f  a  apur-wheel  and  pinion,  the  former  of  which  i-  t"  make 

■j-2  revolutions  per  minute  to  the  others  t.'»J.  what  should  be  thou 
■  radii  f 
We  Ii... i 

>::  R:S9; 
whence, 


and 


win  I , 


,:  MM  often, 


•22  +  15  5 


When  the  pitch  eirehj  radios  of  one  of  tin 

for  the  other  radini  bj 


BOOK   OF    INDUSTRIAL   DESIGN. 


of  the  second  proportion,  for  it  is  sufficient  to  subtract  the  one 
found  from  the  sum  of  both;  thus, 

45  —  26-4  =18-6;  or, 
45  —  18-6  =  264. 
Second  Example. — The  distance,  d,  between  the  two  centres 
being  known  =45  inches,  and  one  wheel  carrying  31  teeth  and 
the  other  44,  what  are  their  respective  radii  ? 
We  have  here,  in  the  first  place, 

45  :  31  +  44  ::  R  :  44; 


whence, 


and 


wdience, 


„       45  x  44 
R=— — -  =  264, 
31  +  44  ' 

45  :  31  +  44  ::  r  :  31; 


45  x  31 
31  +  44 


186, 


or,  more  simply, 


r  =  45  —  26-4  =  18-6  inches. 


In  like  manner,  the  respective  radii  of  a  spur-wheel  and  pinion, 
to  gear  together,  may  be  determined  geometrically,  when  the  dis- 


tance between  their  centres  is  known,  sa  well  as  the  numbers  of 
revolutions  of  each,  by  the  following  rule: — 

Divide  the  distance  into  as  many  equal  parts  as  there  are  of  any 
measure  contained  exactly  in  the  sum  of  the  velocities,  such  mea- 
sure being  also  contained  exactly  any  number  of  times  in  each  of 
the  velocities  alone.  Then,  for  the  pinion  radius,  take  as  many  of 
these  measures  as  are  contained  in  the  lesser  velocity,  and  for  the 
radius  of  the  spur-wheel,  tbje  remainder  of  them. 

Example. — Let  16  inches  be  the  distanco  between  the  centres 
of  a  spur-wheel  and  pinion  which  make  6  and  4  revolutions  re- 
spectively, or  any  equi-multiples  or  equi-submultiples  of  these,  as 
12  and  8,  or  3  and  2.  Divide  the  distance  into  10  equal  parts, 
and  take  4  of  these  for  the  pinion  radius,  and  6  for  the  spur-wheel 
radius. 

This  rule  is  of  very  simple  application  when  the  ratios  of  tho 
numbers  of  revolutions  are  whole  numbers,  such  as  1  :  4,  or  2  :  5 ; 
for  all  that  is  necessary  is  to  add  the  two  together,  to  divide  the 
distance  between  the  centres  to  correspond,  and  to  take  the  re- 
spective numbers  of  measures  for  each  wheel. 

The  following  table  will  be  of  great  assistance  in  the  solution 
of  various  problems  connected  with  systems  of  gearing,  when  tho 
number  of  teeth,  the  pitch,  or  the  radius  are  known. 


TABLE    FOR    CALCULATING    THE    NUMBERS   OF    TEETH   AND    DIAMETERS   OF    SPUR    GEAR,   FROM    THE    FITrH,   OR    VICE    VERSA. 


Namber. 

Coefficient. 

Number. 

Coefficient. 

Number. 

Coefficient. ' 

Nu.be, 

Coefficient. 

Number. 

Coefficient 

10 

3- 183 

39 

12-414 

68 

21-644 

97 

30-875 

126 

40- 106 

11 

3501 

40 

12-732 

69 

21-963 

98  * 

31193 

127 

40-424 

12 

3-820 

41 

13-050 

70 

22-281 

99 

31-512 

128 

40-742 

13 

4-138 

42 

13-369 

71 

22-599 

100 

31-830 

129 

41-061 

14 

4-456 

43 

13-687 

72 

22-917 

101 

32-148 

130 

41-379 

15 

4-774 

44 

14-005 

73 

23-236 

102 

32-467 

.  131 

41-697 

16 

5-093 

45 

14-323 

74 

23-554 

103 

32-785 

132 

12-016 

17 

5-111 

46 

14-642 

75 

23-872 

104 

33-103 

133 

42-334 

18 

5-729 

47 

14-960 

76 

24191 

105 

33-421 

134 

42-652 

19 

6-048 

48 

15-278 

77 

24-509 

106 

33-7411 

135 

42-970 

20 

6-366 

49 

15-597 

78 

24-827 

107 

34058 

136 

43289 

21 

6-684 

50 

15-915 

79 

25146 

108 

34-376 

137 

43-607 

22 

7-002 

51 

16-233 

80 

25-464 

10!' 

34-695 

138 

43-925 

23 

7-321 

52 

16-552 

81 

25-782 

110 

35-013 

139 

44214  . 

24 

7-639 

53 

16-870 

82 

26-100 

111 

35331 

140 

44-562 

25 

7-957 

54 

17-188 

83 

26-419 

112 

35-650 

141 

44880 

26 

8-276 

55 

17-506 

84 

26-737 

113 

35968 

142 

45- 199 

27 

8-594 

56 

17-825 

85 

27-055 

114 

36-286 

143 

45-517 

28 

8-912 

57 

18143 

86 

27-374 

115 

36-604 

1  14 

45835 

29 

9231 

58 

18-461 

87 

27-692 

116 

36-923 

145 

46-153 

30 

9-549 

59 

18-780 

88 

28-010 

117 

37-241 

146 

46-472 

31 

9-867 

60 

19098 

89 

28-329 

118 

37-559 

147 

46-790 

32 

10186 

61 

19-416 

90 

28-647 

119 

37-878 

148 

47-108 

33 

10-504 

62 

19-734 

91 

28-965 

120 

38196 

149 

47-427 

34 

10-822 

63 

20-053 

92 

29-284 

121 

38-514 

150 

47-745 

35 

11-140 

64 

20-371 

93 

29-602 

122 

38-833 

151 

48-063 

36 

11-459 

65 

20-689 

94 

29-920 

123 

39151 

152 

18-382 

37 

11-777 

66 

21-008 

95 

30-238 

124 

39-469 

153 

48-700 

38 

12095 

67 

21-326 

96 

30-557 

125 

39788 

154 

49020 

RULES   CONNECTED    WITH    THE    PRECEDING    TABLE. 

I.  To  find  the  diameter  of  a  spur-wheel,  when  the  number  and 
pitch  of  the  teeth  are  known. 


M  'fiply  the  coefficient  in  the  table,  corresponding  to  the  number  yf 
teeth,  by  the  given  pitch  in  feet,  inches,  metres,  or  other  measures,  and  the 
product  u-ill  be  the  diameter  in  feet,  inches,  or  metres,  to  correspond. 


teeth,  hartrtg  a  filch  of  I*  inches! 

Oppo.it*  lb*  number  60,  ia  lb*  table,  w*  find  the   caaffirln't, 
50-053.    Then— 

20fi53  x  1  i  -  30-08  inches 
the  diameter  of  the  spur-wheel. 

What  an  the  diameter*  of  two  -.heels,  of  41 
:*eth  respectively,  their  pilch  (gang  j  iocs ! 
On  the  one  band,  we  have 

-.:,  =  9-7875  inch**, 
■  the  ilaiaiilii  of  the  pinion  of  41  t«  ih ;  and  on  the  other, 
:  358  inches, 
the  diameter  of  the  spar-wheel  of  15" 

II.  To  find  '  .  spur-wheel,  when  the  diameter  and 

.  are  known. 
Ihnde  tie  firm  diameter  ey  (Jke  aorjuxnt  in  (he  faaJe  um —sums' 
ny  to  tie   number  tf  tie  Met*,  and  tie  quatitmt  via  be  tie  pitch 
tvmgkL 

I         !  Wmm  u  the  pilch  of  a  wheel  of  30-08  inrbee 

diameter,  and  of  63  U-eth  ! 

30-08  :  30-053  =  15  inch, 
the  pitch  n-]u:n-<l. 

SeetmJ  Example. — It  is  required  to  construct  a  »pur-w  heel,  of 
136  teeth,  to  work  with  the  preceding,  what  must  be  its  diameter? 



1-5  x  40-106  =  60-159  ir 
:.' 

I 'I.  T-.  Bad   tin-    t.  hen    the  pitch 

and  diameter  are  known. 

lie  giien  diameter  by  tie  piirn  juA.  tie  number  in  tie 

Isj  •>  ogrramaeJiaj  /•■  tm  fmttmwt  iri..  i«  ::-  mtmhtr  e/lsjn  •    ._-;.'. 

If  ll  I  in  the  table,  take  the  number  earreapond- 

•>at  nearcct  V- 
/Vsf  Examjle. — "Hie  di»n  is,  30-08  inches, 

and  the  pilch  of  the  teeth  u  1'5  inch,  what  number  of  teeth  should 

30-8  :  15=  I 
-:">nd*  to  63  t. 
SeetmJ  Example. — What  should  be  the  number  of  teeth  of  a 
pinion,  the  diameter   of  »l„.  h  u>  875   millimetres,  and  » 
intended  to  gear  with  a  rack.  :»h  u  35  millimetres  ■ 

35. 
The  number  most   nearly  corresponding  to  this  is   110,  the 
to  the  pinion. 


r.LocJTT  or  vntLi 

*■  what  i«  the  anjrvT  me  abaft 

of  *  fly-wheel  •.  r,  iitud  velocity 

rule  :— 

m  by   tie    number   of*  reredutjemt  per 

rnd  tie  prod,.  -    ,porr  pasted  through  n  lie 

tame  time  ;  and  tiit  product  bring  divided  by  60,  via  gim  tie  tab. 

-  nreumferenre  per  tertmd. 

•fiameter  of  a  wheel   be  4  feet,  and   the 


number  of  its  ret  olutioos  par  minute  20,  what  u  the  v . 
th»   I  M  IHfl  n  rx*»r  ! 

The   circumference   of  the  wheel   =  4  x  11416=  1*5664; 
U..  I 

MM  x  20  =  251  328  fret, 
the  apace  paaaed  through  per  minute  by  any  poial  in  the  lin  — 
f ervnee  ;  and 


60 


=  4% 


■ 

..:  the  eirenmference  ia  known,  the  angnlai 
or  the  number  of  turns  in  a  given  lime,  may  be  a-ocr- 
tamed  by  the  following  rale  :— 

Diride  tie  eire^tm/errmtial  Telocity  by  tit  eireutn/eremee,  and  dm 
quotient  trifl  be  He  angular  teiocity,  or  number  rf  read uIhm  in  lit 
giren  time. 

In  the  preceding  rase,  4-3  feet  being  the  circumferential 
per  second,  and  4  feet  the  diameter,  we  hare 

— -il-=33t, 

4  X  3U16  * 

the  angular  velocity  per  second  ;  and 

•334  x  60  =  90, 
■  linute. 
In  practice,  it  is  easy  to  asce-tan.  f  a  wheel,  the 

motion  of  which  is  uniform.     Y  -  marked 

with  chalk  on  the  rim  of  the  ••  w  often 

in  a  .-inn  time;  then 
this  nui  by  the   eircur 

described  by  the  marked  point,  and  the  product  ditided  by  the 
duration  of  the  observation  expressed  in  seconds.  The  result 
will   be  :'  the  circumference*  of  the  wheel. 

I  have  a  AS  rent  ti 
to  its  distance  from  the  centre  of  motion. 
Example. — A  wheel,  2  feet  in  diameter,  baring,  atcoidng  to 
obeu  intion.  made  75  revolutions  per  minute,  what  b  its  cirenm- 
ferential  velocity  (per  second)  ! 

■   3  11x8 


\ 


circumferential  velocity  of  the  wheel. 

-  «-ally.  when  the  circumferential  velocity  (per  secood)  is 
known,  the  ni  ■   .ns  per  minute  is  found  by  means 

ntda — 

V  x  W 
N".(  :i  •   1'  • 
or,  w  ith  the  data  of  the  preceding  esse, 

\  itions  per  minute. 

.  several  spar-wheels  or  pulleys  are  placed  on  the  same 
shaft,  the  cin-  ' 

in  the  name  m. 
the  respective  rircumfcreriees,  and  dividing  lb*  product*  by  60. 

Example. — Three  wheels  on  on* 

shaft ;  the  radios  of  the  pulley,  a,  is  equal  to  1  1  feet ;  that  of  tho 
pulley.  I  that  of  the  pulley.  vod  the  - 

shaft  makes    13  turns  par  minute, — what  is  the 
velocity  of  these  three  pulleys  ! 


BOOK  OF  INDUSTRIAL  DESIGN 


For  the  pulley,  a,  we  have — 

6-28  x  11  x  12 


V  = 

for  the  pulley, 


60 

6-28  x  1-6  x   12 
60 


1-38  feet  per  minute ; 


=  2  feet ; 


arid  for  the  pulley,  c — 

628  x  215  x  12 


=  2-7  feet. 


DIMENSIONS   OF   GEARING. 

220.  In  designing  tooth-gearing  of  all  descriptions,  it  is  neces- 
sary to  determine — first,  the  strength  and  dimensions  of  the  teeth ; 
second,  the  dimensions  of  the  weh  which  carries  the  teeth ;  and, 
third,  the  dimensions  of  the  arms. 

THICKNESS   OF    THE    TEETH. 

221.  The  resistance  opposed  to  the  motion  of  the  wheel  or  the 
load,  may  be  considered  as  a  force  applied  to  the  crown,  to  pre- 
vent its  turning,  and  the  power,  during  its  greater  strain,  as  applied 
to  the  extremities  of  the  teeth.  The  teeth  then  should  be  con- 
sidered as  solids  fixed  at  one  end,  and  loaded  at  the  other ;  and 
the  equation  of  equilibrium  for  thenj  is — 

P  x  l  =  ix  i1  xjc; 
in  which  formula,  P  signifies  the  pressure  in  kilogrammes  at  the 
extremity  of  the  tooth ;  h,  the  amount  of  projection  of  the  teeth 
from  the  web  in  centimetres  ;  A',  a  numerical  coefficient ;  t,  the  thick- 
ness of  the  teeth  in  centimetres ;  w,  their  width  in  centimetres. 

In  this  formula,  the  numerical  coefficient,  A",  which  is  calculated 
with  reference  to  the  motion  of  toothed  gearing,  varies  with  the 
material  of  which  the  teeth  are  constructed. 

From  Tredgold's  experiments  with  well-constructed  cast-iron 
wheels,  this  coefficient  has  been  calculated  to  be  25  for  that 
metal ;  and  adopting  it,  the  preceding  formula  will  then  become 

P  xl  =  25  xl' x  »; 
whence, 

_  25  x  P  to 
h       ' 
a  lormula  in  which  three  dimensions  are  variable. 

The  following  ratios  usually  exist  between  these  quantities : — 

w  varies  between  3  t  and  8  t. 

h  =  l-it  to  15  t. 

Let,  then,  w  =  bt,  and  k  =  1'2  I,  so  that,  substituting  these  values 

in  the  equation,  it  becomes — 


P  = 


25  x  5  x  t  x( 
1-2  x  t 


=  104- x  C; 


whence, 


lot 


and  I  =  -098  \Tp 


11  tne  above  ratio  between  the  thickness,  I,  and  width,  w,  be 
adopted  for  all  proportions  ;  for  low  pressures  or  small  loads,  we 
shall  have  teeth  much  too  thin  and  small ;  and  for  high  pres- 
sures, on  the  other  hand,  the  defects  of  too  great  thickness  and 


pitch.  To  retain,  then,  the  thicknesses  within  convenient  limits,  it 
is  well  to  vary  the  ratio  of  t  to  w,  according  to  the  pressures;  and 
in  order  that  the  pitch  may  not  be  too  great,  the  width  of  the  teeth 
is  determined  at  the  outset,  according  to  the  pressure  or  load 
which  they  have  to  sustain,  in  the  following  manner  : — 


I. 

For     100  to 

200  lb., 

make  w  =     3  t;  when 

= 

1361  I' 

II. 

"        200 

300 

"       w  =  3-5 t      " 

= 

117  ♦'F 

ni. 

"        300 

400 

"      w  =     4 t       " 

= 

no^F 

IV. 

400 

500 

"       w  =  45 1      " 

= 

104  1  P 

v. 

500 

1,000 

"       w  =     5 1      " 

= 

098  fF 

VI. 

"     1,000 

1,500 

"      w  =  55  t      " 

= 

093  ^F 

VII. 

"     1,500 

2,000 

"      w  =     6 t      " 

(  = 

089  VF 

VIII. 

"     2,000 

3,000 

"       w  =  6-5 I      " 

= 

084  ^F 

IX. 

"     3,000 

5,000 

"      w  =     7 1      " 

= 

082  ♦'F 

X. 

"     5,000  and  upwards 

"       w  =     8 1      " 

= 

077  ♦'F 

The  height,  or  projection,  h,  should  be  comprised  between  12  I 
and  15  t,  the  latter  applicable  to  low  powers  or  loads,  and  the 
former  to  high  ones. 

For  teeth  of  wood,  which  are  ordinarily  mado  of  beech  or  elm, 
the  coefficient  should  be  augmented  by  a  tliird  in  each  of  the  last 
given  formula,  which  become — 

I.     I  =  -1G8  /F  making  w  =  3-0  I. 


II.  «=156VF 

III.  i  =  -147  VF" 

IV.  i  =  -139VF" 
V.  Z  =  -131VF 

VI.  t'=-124VF' 

vii.  t  =  -mVP~ 

VIII.  *  =  -112VF" 

IX.  t  =  -109  VW 

X.  t  =  -WA>/F 


to  =  3-5  (. 
w  =  4-0  (. 
w  =  4-5  L 
w  =  50 1. 
w  =  bb  t. 
w  =  6-0  t. 
w  =  6-5  I. 
w  =  7-0  I. 
w  =  80  t. 


All  these  formulas  aro  constructed  on  the  supposition  that, 
although  there  are  generally  several  teeth  in  contact  at  tin-  same 
time,  yet  each  should  be  capable  of  sustaining  the  whole  strain  as  if 
there  were  only  one  in  contact,  and  they  should  be  strong  enough 
to  compensate  for  wear,  and  sustain  shocks  and  irregularities  in  the 
strain  for  a  considerable  length  of  time. 

The  pressure,  P,  on  the  teeth  may  be  determined  according  to 
the  amount  of  power  transmitted  by  the  wheels  per  second  at  the 
pitch  circumference. 

This  pressure  is  obtained  by  di tiding  (he  strain  to  be  transmitted, 
expressed  in  kilogrammitre,  by  the  velocity  per  second  of  the  pitch 
circumference.  A  kilogrammetre  is  a  term  corresponding  to  the 
English  expression,  "one  pound  raised  one  foot  high  per  minute." 
A  kilograminetro  is  equal  to  one  kilogramme  raised  one  metro 
high  per  second  :  it  is  written  shortly  thus — k.  m. 

First  Example. — A  spur-wheel  is  intended  to  transmit  a  force 
equal  to  a  power  acting  at  the  pitch  circumference  of  500  kilo- 
grammetres,  at  the  rate  of  2-09  m.  per  second,  what  pressure  have 
the  teeth  to  sustain  ! 


BOO  k  ■ 


tli»  strain  that  each  I  without 

risk  of  breakage,  even  after  eooaiderahle  use  and  ■ 

SacattJ  Example. —  \  "nnamita 

tea  86  n 

minute,  what  i- 

•  i  r.  =  75  x  30  =  1500  kilugramm.  I 
and 


V  = 


3  14  X  a 
60 


.  per  second; 


1000 


=  573  kilo;-., 


the  preaaure  on  the  tooth. 

ri  at  Ite  crmumferenee 

*  for  tin-  (••■•til  mav  !«•  oalcn 

rding  to  the  material  of  which 

hi  tin-  former  of  the  last  two  examples,  in  which  P  =  239 

iDMal  of  ttio  tOOfh, If  of  Ctat-iroil,  should  be  making 
.  .» I : 

'  =  •117  ♦/239  =  1-8  cent  =  18  millitn.  • 

tample,  when  1'  =  573  kil.,  the  t> 
•Mil  be,  supposing  tin-  teeth  t..  1»-  of  l»  ech,  ud  «•  =  5/, 

I  =  -131  »  673  =  B'M  c,  or  32  3  millim. 

w  =  5  ■    833       loi  :,  ml 

/         ■' 

■ 

It   of  a   spur-v.  ,,  of  wlii.-li  i-   I 

to  detarmini — 0  h  of  this 

apOl  w 

In  1 

7j=  1875  ki: 


V 


1q5  x  2. 


i.       '8™ 

1'         —  =  2113  k,! 


.    a  6*5 1,  the  thickness  of  the  tooth  will  be 

'  =  I  Ml.., 

and 

u>-  MO'SmOUm. 

11  '  '  ir..n  pioJon  of  a  powerful  maohhia 

B.  in  .liamot.T,  il  ii  li\.-.|  OB  I  abaft  Which  should   transmit 

■Unions 

-  tih  nd  ti..  ir  .inn. 

T5  =  15,000  kilogram. 
4ii,| 

.  I     ' 

N  par  second. 


Tbe  pre*-  'h  i»— 

P 

1 1 inking  te  =  6l;  we  bars,  for  the  tlii.  Liuu  of  the 
i,n, 

l  =  -077  4'ti333  =  613  */«. 
and        •  v  =  B 

For  a  pinion  of  tin  ted,  jhq 

■  was  made  75  millim.,  and  the  width  US  nullim. 

. 
•par-wheel  teeth,  measured  on  tin-  pitch  chvumforeoee,  rompriaea 
the  tlii.-kn.— -,  I,  of  tin-  tooth,  and  tin-  width  of  (ha  int.nal,  whi.h 

i  bj  oin.ti -mli ; 
-If.  • 

In  tin-  1st, p  —  31  x  18     =    378  "/. 

3.1 p  =  2  1   x  37     =    777  */_. 

■llli ••  =  2-1   x  61-3  =  128-5  ■/«, 

When  tin-  spur-wl* 

ii, 1  of  il,,-  preceding  examplea,  it  wil 
with  a  pinion,  bsring  eesf-iron  teeth,  which  shook)  !><•  of  about 
Ihree-fourtha  tin-  Ihlrilmnea  of  tin-  a 
)iit.-li  will  Ik-  equal  to  • 

/  +  -75/  +  -1  i  =  1  +  -85  r  =  1 
,n  this  example,  wa  thoukj  hsvi 

p  =  323  X   l-85  =  5'.»8-/_ 
After  this  i-    ■  I  li.-ii  tin-   pHofa  ;.  wlii.li, 

as  has  aln  on  the 

pitch  drclea  of  nny  two  wbeola  woridng  togatbar,  the  Dumber  of 
tooth  of  one  of  the  wheel*  ma**  be  obtained  bj  tl»-  following 
formula  — 

,    of  tin.    spur. win  .1  ;    U.  tho 

i  the  pitch  circle ;  and  /'.  the  pitch,  meaaured  on  ii.  - 

/  /  What  i»  tin-  nni     -  D  .1  spiir-wlii-i-l 

of  two  metres  diameter,  ami  the  pit.li  of  wh 

Ili-r. — 

14  X  1 

N=  ■.,,.,. 

It  will  be  easily  undent I.  thai  the  faction  ariaing  fr..m  the 

D    DlUBl    I 

tooth.     I  fore,  where  I 

must   be  slightly  iocn  I 

deration,  (he  pitch  becomea 

P=    N  —      «»■, 

.  -  m. 

S  /  '       I  rat)    ,'■  .1    to  dl  i.  nninr   tin-  mi' 

w I.  ii  t.  .id  t-.  i»-  BarnV  .1  l.y  a  spnr-wheal  of  two  mi 

the  pitch  b 

II.  n, 

I  I     ■    | 

105. 


BOOK.  OF   INDUSTRIAL  DESIGN. 


When  a  spur-wheel  is  to  have  wooden  teeth,  it  is  necessary 
tnat  the  nuiujjer  of  these  be  some  multiple  of  the  number  of  anus 
of  the  wheel,  in,  order  that  they  may  be  conveniently  attached  to 
the  web ;  thus,  in  the  present  example,  if  the  wheel  is  to  have 
6  arms,  the  number  of  teeth  must  be  102  or  108,  to  be  divisible 
bv  that  number;  and  if  the  former  be  adopted  instead  of  _105,  the 
pitch  will  be  slightly  augmented  in  consequence. 

To  obviate  the  necessity  of  making  long  and  tedious  calcula- 
tions, .a  table  is  subjoined,  showing  the  thickness  and  pitch  of 
teeth  of  spur-wheels,  in  which  is  adopted  the  coefficient  "105  of 
M.  Morin,  which  makes  the  formula, 

for  cast-iron  teeth,  and 

t  —  -145  VT 
for  wooden  teeth  :  the  width  being  constantly  equal  to  nearly  4'5 
the  thickness. 

Table  of  the  Pitch  and  Thickness  of  Spur  Teeth  for  different 
Pressures. 


Of  Cast-iron. 

Of  Wood. 

Kilogrammes. 

Thickness  of 

Teelh  111 
Millimetres. 

Pitch  in 
Millimetres. 

Thickness  of 

Teeth  in 
Millimetres. 

Pitch  in 
Millimetres. 

* 

5 

23 

4-9 

32 

5-9 

10 

3  3 

6-9 

4-7 

8-7 

15 

4-0 

8-5 

5-6 

KV4 

20 

4-6 

97 

6-4 

11-8 

30 

5-7 

12-0 

7-9 

144 

40 

6-6 

13-9 

9-1 

16-9 

50 

7-4 

15-6 

10-2 

18-9 

60 

8-1 

17-u 

11-2 

20-8 

70 

8-7 

18-4 

12-1 

22-4 

80 

9-4 

19-7 

12-9 

23-9       m 

90 

9-9 

20-8 

137 

253 

100 

10'5 

22  0 

14'5 

26-8 

125 

11-6 

24-4 

16-1 

29-8 

150 

12-8 

269 

17-7 

32-7 

175 

13-8       < 

29-1 

191 

34-8 

•Joo 

14-8 

31-1 

.  20-2     . 

37-4 

225 

15-7 

330 

21-7 

40-1 

'J  .'in 

166 

348 

22-9 

42-4 

27  5 

173. 

36-3 

23-9 

412 

300 

18-2 

381 

25-1 

46-4 

S50 

19-6 

41'2 

27-1 

5(rl 

•4no 

21-0 

43-2 

29-0    . 

53-6 

: 

23-4 

49-1 

32-4 

59-9 

600 

25-7 

640 

355 

65-7 

700 

27 '7 

582 

37-2 

69-1 

soo 

29-7 

G2-4 

41-0. 

75-8 

900 

315 

66-1 

43-8 

83-0 

1000 

332 

69-6 

45-8 

84-7 

•  With  the  assistance  of  this  table,  and  the  preceding  rules,  we 
can  always  determine,  not  only  the  thickness  and  pitch  of  the  teeth, 
but  also  their  height  and  width,  since  these  are  in  proportion  to 
their  thickness. 

DIMENSIONS   OF    THE    WEB. 

223.  The  width  of  the  web  is  ordinarily  equal  to  that  of  the  teeth 
when  the  whole  is  of  cast-iron.  Nevertheless,  in  some  cases — such 
as.  for  example,  where  very  great  irregularities  in  the  pressure  and 
speed,  and  reiterated  shocks  have  to  be  borne  in  the  heavy  ma- 
jhinerv  in  engine  shops — the  web  is  made  wider  than  the  teeth, 


projecting  also  on  either  side  of  the  teeth,  so  that  these  are  wholly 
or  partially  imbedded,  which  increases  their  power  of  red 
very  considerably.     These  lateral   webs  are  generally  each  made 
oT  about  half  the  thickness  of  the  tooth. 

The  thickness  of  the  web,  or  crown,  is  never  made  less  thai! 
three-fourths  that  of  the  tooth,  and  very  frequently  it  is  further 
strengthened  by  an  internal  feather,  as  already  mentioned 

213.  When  the  teeth  are  of  wood,  the  web  is  much  thicker,  to 
give  sufficient  hold  to  the  tenons  of  the  teeth;  it  is  generally 
made  about  l-5  to  2'  times  the  thickness  of  the  tooth. 

NUMBER   AND   DIMENSIONS  OF    THE    Aims. 

224.  The  number  of  arms,  or  spokes,  which  a  Bpur-wheel 
to  have,  has  not,  up  to  the  present  time,  been  precisely  aid 
scientifically  determined.  According  to  general  experience,  up  in 
a  diameter  of  1  me:tre,  or  about  3.  feet,  four  arms  are  sufficient; 
from  1  metre  to  2  metres,  or  3  feet  to  6  or  7  feet,  aix  are 
necessary  and  sufficient ;  beyond  2'5  m.,  or  8  feet,  eight  arms  ai  e 
used:  and  for  5  m.,  or  16  feet,  ten  are  given;  it  is  seM 
last  number  is  exceeded,  except  for  wheels  of  extraordinary  di- 
mensions. 

The  section  of  the  arms  of  the  wheel  is  always  in  the  form  of 
a  cross,  the  stronger  portion  of  which  lies  in  the  plane  of  the  cir- 
cumferential strain,  whether  these  aims  are  cast  in  one  piece  with 
the  boss  and  the  crown,  as  is  the  case  with  wheels  oi  small 
diameter — that  is,  of  such  as  have  not  a  greater  radius  than  2  m.  or 
6i  feet;  or  whether  they  are  cast  in  separate  pieces,  and  after- 
wards fitted  together.  The  thicker  part,  then,  of  the  arm  must  he 
strong  enough  to  bear  the  circumferential  strain.  Experience 
has  shown,  that  when  a  spur-wheel  is  in  motion,  and  acted  upon 
by  a  considerable  force,  this  strain  has  a  tendency  to  make  the 
arms  assume  a  twisted  shape,  and  produce  on  them  a  lateral 
inflexion.  It  is  to  obviate  and  prevent  this,  that  the  arms  aro 
strengthened  by  feathers. 

The  power  acts  with  greatest  effect  near  the  boss  of  the  wheel, 
so  that  it  is  necessary  to  make  them  wider  at  this  part  than  near 
the  crown,  so  as  to  approximate  to  the  form  which  presents  an 
equal  resistance  throughout  This  will  be  observed  in  the 
figures  in  Plate  XX.  The  boss  must  have  such  a  thickness  as 
will  allow  of  the  wheels  being  solidly  fixed  on  the  shall.  A 
thickness  of  5  inches  maybe  considered  a  maximum  for  the  bossi  s 
of  moderately-sized  wheels.  The  dimensions  of  the  arm- 
be  in  proportion  to  the  width  of  the  web  or  crown,  their  thickness 
being  ordinarily  about  J  that  of  the  crown.  This  proportion  i^  a 
good  one  for  wheels  under  6*  feet  in  diameter.  For  larger  sizes, 
i  the  width  of  the  web  is  considered  sufficient 

The  lateral  feathers  should  have,  at  the  very  most,  only  the 
thickness  of  the  arm.  Generally,  the  width  of  the  arm  near  the 
web  is  made  about  §  of  its  width  near  the  boss.  The  following 
table,  calculated  from  Tredgold's  experiments,  shows  the  propor- 
tions to  be  given  to  the  arms  or  spokes  of  spur-wheels,  ace 
to  the  strain  acting  at  their  circumferences;  supposing  the  dia- 
meter of  the  wheels  to  be  1  m.,  and  the  number  of  arms 
thickness  being  taken  equal  to  J  the  width  of  the  crown.  The 
dimensions  given  are  the  averages,  or  those  to  be  applied  to  tlio 
arm,  half-way  between  the  boss  and  the  crown. 


Tin:  I'iimth'ai.  imu  ciirsMws 


Tabk  e/fJkt  Dimauiau  </  Spur.r\nl  Arms. 


•  a.i-t 

IV  -Iik   »f  lk*  Arm  u 
fMUawm 

W«hk  om  aft,  of  lk. 

I'..'.h»r«    la    fatiaWllaa. 

4  "DO 

1    .'1 

6-00 

SO 

8-50 

144 

1 

■ 

1!   •   I 

is  ia 

1310 

1 

• 

1310 

II  M 

■ 

i:  I ' 

11     ■ 

l  • 

To  »p[>!v  the  numbers  in  t; 

I         »    It,  R  In  iiii.'  tho   ra.lius  of  (lie  whc.-l 
fur  which  ill-  dimensions  arc  to  bo  calculated. 


W0ODCI    riTTEBX*. 

I  canting  has 
doced,  :. 

be  turtn-d,  I 

this  laal  MM,  an  lli« 
allownm 

uld  Iw 
given. 

j   mathematical  precision — w 
i«,  that, 

:.  that,  in   liH. 
loam,  tin-  moo 

y  at  all 
part*.     Willi  regard  !•>  (In-  la 

1 1  n  foaiid  thai  tho  diameter  of  a  win 
tin-  line  of  the  amis,  i«  noaibly  less  tluin  M 

• 
-.  that  in  ttle  I 
-  a  M\t!i  of  an  ineli. 

nanifeat,  that  all  il>  ma  moat  be  bona  in 

mind  whan  constructing  wooi  y 

errors  at  magnitada  will  arise. 


CHAPTER   VI. 


ITINUATION   OF  THE   STUDY   OF  TOOTHED   GEAR, 


•  only  capable  of  tnmamitting 

which  are  |ianillil  to  each  other;  and  when 

1.  ..r  form  any  angle  with  each  other,  tin- 

to  be  made  conical,  ami  are  than  caBad  l«-vil- 

■  of  gear  may  In-  capable  of  working 
■!v.  ami  of  ti  riderable  power  whan 

•  ar,  it  i*  eaaontial  iliat  the  ahafta  or  as  ■  of 

any  pair  work!  ■  in  tins 

v.il  mi«t  in  a  point  which  i<  tl»-  apei  common  to 

n  throogh 

khaTU  i:  •  .  other  at  right 

■  couple 
barn  for  teeth,  paaaing  from  one  to  tie-  other 

parallel  to  the  axis  ;  and  the  wheal  to guar  with  thi- • 
10   parnllil  with   the   n\i-,  1"'' 
from  a  - 

it  when 

at  for  aome  d-  -  .ning  machinery — the 

■  frame,  for  example — bvvil-wheele  are 


i  ahnata  in  the  eame  plane ;  th< 
termed  "-ki  «  bevila,"  from  the  teeth  having  a  hyporboloida)  twist 
in  order  that  they  may  net  pr  I        kind  of 

wheel  doM  not  work  well,  and  la  asldom  employed,  except 

■ 
mlttod :  the  pwliT  fonn  rd  (hi  b  I 
difficult  to  eonatrnet    Their  dm  it  so  limited,  that  ftvtai  i 

for.     Indeed,  they  ought  rather  to  lw 
avoidi  'i  m  Im\  il- 

wli.  ela  cannot  I  for  them  with  adranl 

teeth  of  bovB  ie  of  wood  or  meUl,  abnOarly 

to  epur-wbeel  teeth,  and  thou  rma  are  detera 

axa  i*  unit. 
I'i.in:    xmi. 

• 

«Ih  al  a Ian  t.  eth,  and  thi 

I  ii  the  pair  of  •pur-wl 
Let  I  the  two  wheala 

aaaumed   here  to  be  at  right  anglca  to  aaah  "tier .   though  we 


BOOK   OF   INDUSTRIAL   DESIGN. 


71 


must  observe,  that  what  follows  will  apply  equally  well  to  the 
construction  of  a  couple  of  wheels,  the  axes  of  which  make  any 
angle  with  each  other,  acute  or  obtuse. 

Let  B  D  =  '220  m.,  and  ef  =  -440  m.,  the  radii  of  the  pitch 
circles  of  the  two  wheels.  It  is,  in  the  first  place,  necessary  to 
determine  the  position  these  circles  should  occupy  on  their  respec- 
tive axes.  With  this  view,  on  any  point,  B,  taken  on  the  axis,  A  B, 
erect  a  perpendicular,  B  D,  and  make' it  equal  to  the  radius  of  the 
smailer  wheel,  and  through  the  extremity,  D,  draw  a  line,  D  L, 
parallel  to  this  axis ;  in  the  same  way,  at  any  point,  e,  taken  on 
the  axis,  A  c,  erect  the  perpendicular,  E  F,  equal  to  the  radius  of 
the  larger  wheel,  and  through  the  extremity,  r,  draw  F  n  parallel 
to  A  o.  The  point  of  intersection,  G,  of  these  two  lines,  F  H  and 
n  l,  is  the  point  of  contact  of  the  two  pitch  circles,  the  radii  of 
which  are  g  i  and  g  k.  Blake  i  h  and  k  l,  respectively,  equal  to 
the  radii,  and  join  the  points,  H  G  L,  to  the  common  apex,  A,  thereby 
determining  what  are  termed  the  "  pitch  "  cones,  A  H  G  and  A  G  L, 
of  the  two  wheels,  the  straight  line  or  generatrix,  A  G,  being  the 
line  of  contact  of  the  two  cones.  These  pitch  cones  possess  the 
same  properties  as  the  pitch  circles,  or,  more  correctly,  pitch 
cylinders,  of  spur-wheels ;  that  is  to  say,  their  rotative  velocity  is 
in  the  inverse  ratio  of  their  diameters,  and  their  diameters  are  pro- 
portional to  the  respective  numbers  of  their  teeth. 

The  proportions  of  the  pitch  cones  being  thus  obtained,  with  the 
centres,  o  and  o',  figs.  2  and  3,  taken  on  the  prolongation  of  the 
given  axes,  describe  the  pitch  circles,  A  h'  i'  and  g'  k'  l'.  Divide 
these  circles  into  as  many  equal  parts  as  there  should  be  teeth  ; 
that  is  to  say,  in  the  present  case,  24  and  48,  respectively,  which 
operation  will  give  the  pitch;  each  part  is  then  bisected  to  obtain 
the  centres  of  the  teeth  and  of  the  intervals,  and  on  each  side  of 
the  centre  lines  are  set  off  the  demi-widths  of  the  teeth,  regard 
being  had  to  the  difference  to  be  made  between  the  wooden  and 
cast-iron  teeth,  as  already  explained  (213). 

The  external  contours  of  the  teeth  will  be  situated  in  cones,  the 
generatrices  of  which  are  perpendicular  to  those  of  the  pitch  cones ; 
they  are  obtained  by  drawing  through  the  point  of  contact,  G,  on 
the  line,  a  g,  a  perpendicular,  b  c,  meeting  the  axis  of  the  smaller 
wheel  in  B,  and  that  of  the  larger  one  in  c ;  the  points,  B  and  c,  are 
the  apices  of  the  two  cones,  B  H  G  and  c  G  L. 

If  these  last-mentioned  cones  be  developed  upon  a  plane,  it  will 
be  easy  to  draw  upon  it  the  exact  forms  of  the  teeth.  Now,  we 
have  seen  (170)  that  the  development  of  a  cone  on  a  plane  surface 
takes  the  form  of  a  sector  of  a  circle,  which  has  for  radius  the 
generatrix  of  the  cone,  and  for  arc  the  development  of  the  base  of 
the  cone.  As  it  is  unnecessary  to  develop  the  entire  cone  in  the 
present  case,  it  is  sufficient  to  describe  with  any  point,  b',  fig.  4, 
with  a  radius  equal  to  b  g,  an  arc,  a  e  b,  on  which,  starting  from 
the  point,  c,  are  divided  off  distances — one,  c  d,  equal  to  the  thick- 
ness of  the  tooth  of  the  smaller  wheel,  fig.  3,  and  the  other,  c  e,  to 
that  of  the  tooth  of  the  larger  wheel,  fig.  2.  The  same  operation 
is  performed  for  the  larger  wheel ;  that  is,  with  the  point,  c', 
situated  on  the  prolongation  of  b'  c,  and  with  a  radius  equal  to  c  g, 
describe  the  arc,  / eg,  on  which  are  measured  the  distances, 
respectively,  equal  to  the"  former  ones,  e  d  and  c  e. 

This  dune,  the  outlines  of  the  teeth  are  obtained  by  means  of 
precisely  the  same  operations  as  those  explained  in  reference  to 


tho  spur-wheels.  Thus,  on  the  radius,  e'  <-,  considered  as  a 
diameter,  describe  a  circle,  i  cj,  which,  in  rolling  round  the  circle, 
f  e  g,  considered  as  the  pitch  circle  of  the  larger  wheel,  determines 
the  epicycloid,  e  h,  which  gives  the  curvature  of  the  teeth  of  the 
larger  wheel  ;  in  (he  same  manner,  the  circle,  k  e  I,  described  on" 
the  radius,  e  c',  as  a  diameter,  and  rolling  round  the  circle,  a  c  b, 
gives  the  epicycloid,  c  m,  which  is  taken  for  the  curve  of  the  teeth 
of  tho  smaller  wheel.  After  having  repeated  these  curves 
metrically  on  each  side  of  the  teeth,  these  are  limited  by  drawing 
chords  in  tho  generating  circles  from  the  point,  e,  each  equal  to 
the  pitch  of  tho  teeth,  as  c  n,  c  k,  and  then  with  c'  and  i,'  as  centi  i  - 
describe  circles  passing,  one  just  outside  the  point,  n,  and  tho  othvr 
just  i«itside  tho  point,  k ;  and  to  indicate  tho  line  of  the  web,  describe 
a  second  couple  of  circles,  nearly  tangents  to  the  preceding.  Then 
project  the  points,  o  and  p,  which  indicate  the  depth  and  extre- 
mities of  the  teeth,  over  to  the  line,  B  c,  in  o  and  p  ;  through  theso 
last  draw  straight  lines  to  the  apex,  a,  which  will  represent  the 
extreme  generatrices  of  the  teeth,  as  in  vertical  section. 

As  all  the  teeth  converge  in  one  point,  it  is  obvii  us  that  tho 
contour  of  the  inner  ends  of  the  teeth  cannot  be  the  same  as  that 
of  the  outer  ends ;  the  difference  is  the  greater,  according  as  the 
width,  g  r,  on  the  generatrix  line  of  contact  is  itself  greater,  in 
proportion  to  the  entire  cone,  and  to  the  greater  or  less  angle 
formed  by  the  extreme  generatrices. 

In  other  respects,  this  contour  is  determined  in  the  same  manner 
as  the  first,  Thus,  through  tho  point,  r,  is  drawn  the  straight 
line,  s  t,  perpendicular  to  a  g,  which  cuts  the  two  axes,  and  givi  9 
the  proportions  of  the  two  cones,  on  the  surface  of  which  lie  the 
contours  of  tho  inner  ends  of  the  teeth.  Continuing  the  opera- 
tion as  above,  portions  of  the  cones  are  developed,  arcs  being 
described  with  the  points,  s'  and  (',  as  centres,  and  radii  equal  to 
r  s  and  r  I.  The  diagram,  fig.  5,  which  is  analogous  to  fig.  4,  fully 
explains  what  further  is  to  be  done. 

What  has  been  said  so  far,  has  referred  only  to  one  tooth  of 
each  wheel.  In  proceeding  with  the  execution  of  the  design,  after 
cutting  out  templates  to  tho  form  of  the  teeth  as  obtained  by 
means  of  them,  the  outline  is  repeated,  as  often  as  is  necessary,  on 
the  external  cones,  the  generatrices  of  which  are  B  G  and  G  c,  for 
the  outer  ends  of  the  teeth,  and  on  the  internal  cones,  the  genera- 
trices of  which  are  r  s  and  r  t,  for  the  outlines  of  the  inner 
the  teeth.  At  tho  same  time,  and  in  order  that  the  operation 
may  be  performed  with  regularity,  a  series  of  lines  should  be 
drawn  through  the  points,  o,  p,  of  the  two  wheels,  lying  on  the 
surface  of  the  external  cones,  a  h  g,  a  g  l,  and  uniting  at  tho 
apex,  A,  by  means  of  a  "false  square."  of  a  form  analogous  to  that 
represented  at  x,  in  fig.  3,  Plate  XXIII.,  for  the  smaller  wheel, 
and  like  that  represented  at  T,  fig.  4,  of  the  same  Plate,  for  the 
larger  wheel. 

The  forms  of  the  teeth  being  thus  obtained,  the  partial  section, 
fig.  1,  of  fhe  two  wheels  is  drawn,  the  radii  of  the  shafts  being 
given,  as  well  as  the  thickness  of  the  bosses  and  Webs,  the  propOf 
tions  employed   in   the   present    example  being  indicated  on  tho 

drawings.      It  will  be  observed  that  those  teeth  which  are  of« 1 

are  adjusted  in  the  web  of  the  larger  wheel,  in  the  same  luaniiet 
as  in  the  spur  or  cylindrical  wheels,  the  forms  of  the  tenons  being 
modified,  so  that  their  sides  all  incline  to  the  common  apex,  a 


TIIK    I 


TV  erctioasv  together  wtth  the  developnienta,  fig*.  4  and  S.  are 
•urfirirol  for  the  parpeeea  of  construction,  a*  all  the  required  mea. 
earesaeata  en  be  obtained  from  them ;  but  when  it  b  desired  to 

will  be 
■ns  of  the   teeth   and   other  parta.  ' 

•  tally  drawn  D| 
-•  -  of  tin-  whc.  K  M 

Ij    bean 

- .  als,  and  mart 

i  and  I  •    '  ' 

,  limit*  the  lower  ntel  oul 

■   • 

t  I  which  the  p  In  thi* 

circle,  a  - 

■ 
■ 

•  to  the  centre, 
.  found  in  a  similar  HaW,  draw  similarly 
■ 

ir  an-   to  represent  tin-  epicycloids!  curve, 
une  time 

TV  '  in  fio-.  3  :   It  OOMbta  in  dmw- 

or.  and  rd,  r  i/,  by  a   pcr|>eiiiiicular   i 

• 

'i  on  the 
mpleted  by  d 
area  for  the  corresponding  i 

drawn  i  ling  to  r  anil  |  ' 

tweea  lha  teeth — thai 
drawn,  1 1 1 • »  proj<  ctiu/ia  of  the 
•    ■ 
ii.     It  will  V  obaarred  that,  on  i 
I  a  view  of  n  quarter  "f  the  lower  and  inner 
portion    of  thl 
:li  a*  in  plan  ;  in  the  former  • 
■ 
I  web  on  which  wt  are  look  rat  ud 

■  ■I  the  teeth  of  the  mall 

ling  or  squaring  orer,  from 

to  tli-   pit.  h   line,  ■•  n  ;  nn.l 
over   thi  to    the 

I 
• 

flank*  at 

.  ami  it 


termediate  brtwprn  u,  p,  and  e,  e,  may  be  obt.. 

Ii  are 
■ 
in  fie;.  3.     Tin. 

in^'  In  the  apex.  A,  and  find  the  latere 
of  the   • 
and  jf . 

I  the  teeth  m 

I 

■|>er  left -haii  d 

whole 

r.  of  the  arc,  whi. !. 
portion  of  each  tooth,  is  shown  in  fig.  H".      Kr..iu  th  • 
are  obti  lir.-d  to  produce  ti- 

i  in  fig.  I.     TV  operation*  an 

wheel;  -ire  also  used  to  | 

■irity. 

■  nds  at   K  a  second  quadrant 
of  tin-  win-el.  drawn  as  seen  from  U 

-  Mrh  all 
\   third  quadrant,  r. 

:.  so  that  the  mordant  art  -  :ant,  r, 

■ 
I  i   th"  amis  ot   - 

rough  the  li-  i  of  the 

web  made  through  Dm  Baa,  :t — i.  igh  the 

centre  r.f  the  mortise  ;  and  fig.  8  comprehends  a  lateral  i 
and  !'• 

r-wheela,  an-  t      I 

Tin-  n  .  -ill  enable  tin 

to  fom  an  accurate  id.  a   ot    the   actual   proportiona  of  1 1 . . 

mi.  .  oatrat  •  ma  n  an*  <  i-air 

OF    III 

Will. 

• 

-till,  at  lha  ... 

the  difference  in  the  form  of  the  l. 

y..  in. 

I     -i  2  repn  -  nl  ;>,.   •  iwttern 

of  the   two  wheels  in  the  p  1 

is    a  \  i  : ' 

,  nt  roughly  log*.  Ihar,  ud  tnu 


BOOK   OF   INDUSTRIAL   DESIGN. 


form  the  crown ;  and  on  the  other,  a  view  of  the  same  as  finished, 
with  the  arm  and  its  feathers. 

It  will  bo  seen  from  these  figures  that  the  crown  is  built  up  in 
the  same  manner  as  that  of  the  pinion  in  Plate  NXI. ;  the  layers 
of  wood  are,  however,  in  steps,  increasing  iu  diameter  downwards, 
so  as  to  give  the  required  conical  form  when  turned.  When  these 
pieces  are  glued  together,  the  whole  is  turned  externally  and 
internally  in  such  a  manner  as  to  conform  exactly  to  the  full-sized 
drawing,  previously  made  on  a  board  planed  smooth  for  the  pur- 
pose. "  Squares,"  also,  should  be  made  from  the  drawings,  to 
serve  as  guides  in  producing  the  correct  conical  inclination. 

After  turning  the  top  face,  b>  b',  perpendicular  to  the  axis  of  the 
cone,  the  pattern-maker  proceeds  to  turn  the  external  conical 
surface,  a'  b',  of  the  web  or  crown.  As  a  guide  in  doing  this,  he 
takes  a  "  false  square,"  T,  fig.  4,  of  which  one  side,  b  b,  corresponds 
to  the  plane  face,  4'  b',  and  the  other,  a  b,  to  the  inclination 
of  the  conical  generatrix,  a'  b' :  it  is  very  easy  with  this  to  take 
off  just  as  much  of  the  wood  as  is  necessary,  without  the  liability 
of  going  too  far.  It  is  also  necessary  to  determine  the  inclination 
of  the  generatrix,  b  a',  of  the  outer  cone,  perpendicular,  it  will  be 
recollected,  to  the  contact  generatrix,  G  r,  by  means  of  the  square, 
x,  fig.  3,  the  side,  a  b,  of  which  is  applied  exactly  to  the  conical 
surface,  a'  b',  and  the  side,  a  c,  then  gives  the  inclination  of  the 
conical  surface,  a'  c' ;  and  the  same  square  being  turned  round  will 
give  the  inclination  of  the  internal  conical  surface,  b'  d',  the  gene- 
ratrix of  this,  the  smaller  cone,  being  s  r,  parallel  to  B  G,  that  of 
the  larger  one.  " 

Finally,  the  thickness  at  a'  c'  and  V  d',  is  measured  on  the 
wooden  web,  so  as  to  obtain  the  proportions  of  the  internal  conical 
surface,  c  d',  to  be  turned  out  in  a  similar  manner. 

Mortises  have  now  to  be  cut  in  the  crown  to  receive  the  ends  of 
the  arms,  c,  and  their  feathers,  E.  As  the  wheel  under  considera- 
tion is  of  very  small  diameter,  the  number  of  arms  is  limited  to 
four;  these  arms  are  so  placed  inside  the  crown  that  the  feathers 
are  all  on  one  side,  and  towards  the  wider  end  of  the  cone.  Their 
attachment  to  the  web  is  by  means  of  a  circular  groove  or  mortise, 
seen  at  e'f,  fig.  2,  and  at  g'  d',  fig.  3,  and  they  are  united  at  the 
centre  to  each  other  and  to  the  boss,  in  the  same  manner  as  the 
arms  of  the  pinion,  described  in  reference  to  Plate  XXI.  The 
arms  are  not  placed  in  the  middle  of  the  boss,  as  in  the  spur-wheel 
and  pinion,  but  are  simply  applied  to  the  base  of  the  boss,  which 
may,  consequently,  be  of  a  single  piece ;  and  the  feathers  are  let 
into  a  groove  extending  their  whole  length,  and  are  fixed  into  the 
boss  and  crown  at  either  extremity.  The  boss  is  slightly  coned, 
so  as  to  give  the  "draw"  necessary  in  the  construction  of  the 
mould.  Its  outer  edges  are  indicated  by  the  lines,  m  n,  m  n,  whilst 
the  other  lines,  o  p,  which  are,  on  the  contrary,  parallel  to  the  axis, 
show  the  depth  of  the  grooves  cut  to  receive  the  feathers  of  the 
arm.  These  last,  as  shown  in  the  section,  fig.  10,  are  thicker  near 
the  arms. 

The  core  pieces,  E,  are  added  on  either  end  of  the  boss,  and  the 
whole  is  held  firmly  together  by  means  of  a  central  bolt. 

The  pattern  being  so  far  advanced,  the  external  conical  surface 
is  divided  into  as  many  equal  parts  as  there  are  to  be  teeth  and 
intervals,  and,  with  the  assistance  of  the  "false  square,"  t,  lines 
which  represent  generatrices  of  the  cone,  are  drawn  through  the 


points  of  division,  to  indicate  the  positions  of  the  teeth  or  of  the 
grooves  to  receive  them. 

Each  tooth  is  cut  out  separately  according  to  the  fall-size  draw- 
ing made,  as  already  mentioned,  which,  besides  containing  the  ver- 
tical section,  fig.  3,  should  also  show  the  exact  form  of  each  end  of 
the  tooth,  e',  and  of  the  dovetail  joint  attaching  them  to  the  web. 
Fig.  5  shows  a  portion  of  this  drawing  for  the  larger  ends  of  tho 
teeth. 

PATTERN  OF   THE   LARGER   BEVIL   WHEEL. 

230.  Figs.  6  and  7  represent  the  elevation  and  plan  of  tho 
pattern  of  the  larger  bevil  wheel,  with  wooden  teeth,  represented 
in  Plate  XXII.  Fig.  8  is  a  vertical  section  through  the  axis  of  the 
wheel,  showing  on  one  side  the  arrangement  of  the  pines  of  wood 
built  up  upon  one  another,  and  forming  the  crown,  a,  and  on  tho 
other  side,  the  same  piece,  turned  and  finished,  attached  by  tho 
arm,  c,  to  the  boss,  D. 

Fig.  9  represents  the  false  square,  T,  employed  as  a  guide  for 
giving  the  proper  inclination  to  the  external  conical  surface,  <i  //, 
of  the  crown. 

Fig.  1 1  is  a  transverse  seetion  of  one  of  the  arms,  or  spokes, 
taken  through  the  line  7 — 8  in  fig.  7. 

Whatever  explanations  are  called  for  regarding  the  construction 
of  the  crown,  a,  the  arms,  c,  and  the  boss,  D,  as  well  as  the  uniting 
of  these  parts  with  each  other,  have  already  been  given  in  reference 
to  preceding  examples.  We  have  distinguished  all  corresponding 
parts  and  working  lines  by  the  same  letters. 

The  only  difference  between  this  last  and  the  preceding  example 
consists  in  the  disposition  of  the  tooth  pieces,  b',  placed  on  the  out- 
side of  the  crown,  to  form  the  sockets  in  the  mould  for  i. 
the  core  pieces  for  the  mortises,  into  which  the  wooden   teeth  are 
to  be  fixed  after  the  piece  is  cast. 

It  must  be  observed,  in  the   first   place,  that  these   projections 
must  be  shaped  so  that  the  end,  k  I,  is  inclined  to  the  surface,  b'  a, 
instead  of  being  perpendicular  to  it.     This  inclination  must  be 
sufficient  to  allow  of  the  easy  disengagement  of  the  piec 
the  mould.      This   disposition   is   necessary,   because    th 
half  of  the  mould  takes  the  impression  of  the  outside  of  the  crown, 
with  the  tooth  pieces  and  the  upper  portions  of  the  arms,  whilst 
the   top  part   of   the   mould    takes  the   inside  of  the  crown,  the 
feathers  of  the  anus,  and  the  boss,  the  position  of  the  who 
the  reverse  of  that  in  which  they  are  represented  in  the  drawing. 

The  core  pieces  for  the  teeth  are  formed  by  the  moulder  in  core 
boxes,  similar  to  those  described  in  reference  to  figs.  10  and  11, 
Plate  XXI.,  which  we  have  reproduced  in  Plate  XAjLLL,  figs.  12, 
13,  and  14,  as  modified  to  suit  the  different  form  of  tooth.  Fig. 
12  is  a  face  view,  and  figs.  13  and  14  are  sections  made  through 
the  lines  9—10  and  11—12  of  fig.  12.  It  will  be  observed  that, 
at  the  larger  end  of  the  tooth,  the  part  to  project  is  formed  with 
an  inclination  corresponding  to  k  I,  in  fig.  7,  already  referred  to  as 
required  in  this  case. 

The  operations  called  for  in  delineating  these  patterns  are  all 
fully  indicated,  and  are  analogous  to  those  in  the  preceding 
The  observations,  also  (149  and  214),  already  made,  with  reference 
to  calculating  tin-  allowance  to  be  made  for  shrinking,  and  for  tho 
turning  and  finishing  processes,  are  equally  applicable  to  the  case 
before  us. 


N 


T1IK    PRACTICAL 


I\\  >  HELICAL  TEETH 

SSBXJ  with 


i— «■»!.  win-rein 
rved — 

•ii-  without  dc-tcriunit- 

3ti.  ■; 

it  varies  throughout  the  duration  I  :  from 

which  i'  egubrity  in  the  action  and  inequality 

.mount  of  friction. 

1USM  have  induced  a 

■    of  the 
m  tried.    Tin-  ban  in  question  possesses  the  fol- 
lowing : 

1  bo  ban  of  thi  '  i  wheel  hi  quite  Independent 

o  ■  • 

.  Uiu  centres  of  the  wheels,  may  be 
I 

author*  also  attribute  to  this  form  the  property  <>f  trans- 
mitting '  .  boot  the  duration  of  I 

tact.     'I' 

of  tin-  ;  ■  wheeb  is  constantly 

ariation  not  being  accurately  proportions]  in  the  two 
1 

-••so  and  o',  fig.  1,  uf  tlie  two  wheeb  be  given, 
raiiii,  o  a  and  a  of,  ol  cb  circles;  also, 

•.  a  n,  passing  througb 

-,  a.  and  prolong  it  indefinitely  b  \  Prom 

-  line  a  perpeodbubr,  o*  <•,  ><n  which 

will  accordingly  !»•   tin-   radius  of  u  SOOOnd  circle   tangent   tO  Uiu 

same  line.     These  cir. 

.  re  d<  ris.-.i  the  bvol  i  and  c  </.  forming  the 

outline  I  the  wheeb  nro  drawn  just  as 

KVHL  ('197.) 
It  nwst  be  obeerred  tbat  the  eurve,  a  6,  which  i*  th>-  bvolata 
■  a,  i-  thai  for  tl»-  both  of  the  apur- 
h  i'  the  MnMi  and  the  radius,  o  a  ;  and,  in 

i  eurve,  r  (I,  tin-  inviiliit.-  nf  tin-  amaller  • 

D  of  the  radius,  n'  a.      It  tliu-  | 

that  the  f..nn  ;  the  apm>whee)  ■  qnJb  bdependi  nt 

of  the  dbmeter  of  the  pinion,  whflat  that  of  ma  |>iiii..n  both  is 

;  of  the  tpmvwbeeL    from  whbh  b 

notrnctod  in  this  manner  nan, 

witii  at  •  ',  an  formed  on  the  name  prindpbi 

and  wfaOH    pibfa    is   tlie   sainc,  w|i: :■■ 

-    n..t    nilrnit 


I  .-obi  are  large,  and  t   - 

■  -,  a  b  and  e  J. 

I 
'     ■ 

the  common  tangent,  a  b,  a  < 

./.li  the 

will  1«-  tin-  externa]  limit  uf  the  pinion 

In  like  ruann  on,  a  -  .  of  |] 

•    a  distance,  A  c',  also  eqneJ  b  the  pitch, /g,  and  with  tlu< 
■ 

th.      It  is  I'urtl,-  • 
paeilim  a  little  within 
on  tin-  other,  «iil  determine  the  depth  of  t)  the  lino 

b  nf  the  pinion  and  spur-wheel  respectively. 

I  is  a  diagram  to  show — first,  how  thai  tin 

I  omtnofl 

.  ii  i-.     Thus,  n 
pbion  tn  turn  in  the  ilir.s-li.in  of  the 
as  A  of  the  involute!  a  h,  ia  m  the 

0  .  of  the  pinion,  whilst  it  ui  : 

the  centre,  o,  of  the  spar-wheoL    Returning  to  Bg.  3.  it  is  ahowBi 
in  the  eeeond  place,  that  the  distal 

,  Is-  v.-iri.-.l  without  it- 
but,  in  in  h  case,  the  inclination  of  the  t..-, 

xs  u  i  ,  when  Uie  two  centres  are  : 
nearer  to 

In  practise,  I   rmining  the  radius,  o  B,  arbitrarily, 

and  then  deriving  tlu-  other  radius,  n  o,  from  it,  or  mm  tma,  th» 
efaebe  which  am  for  generating  the  bvotutee  may  !»•  found,  an 
well  as  the  inclination  of  the  tangent,  by  the  following  method  i — 
On  one  of  the  pitch  circles,  thai  of  the  pinion,  for  example,  take 
an  are,  a  i,  anajaj  to  the  pitch  of  the  teeth;  draw  the  r.i 
and  on  it  let  fall  a  perpendicular,  a  m.  from  the  point,  a  :  o  m  will 
then  Ih-  tin-  radius  of  the  generating  circle  for  the  mvolota  sum 

Of  the  teeth  of  the  pinion,  and  by  prolonging  m  A  to  n,  which  is  in 

common  tangent,  and  drawing  the  radhm,  o  a,  porpondl- 

cular  to  it,  or.  what   is  the  same  thing,  parallel  to  o'  m,  <i  n  will  Ixj 

the  radius  of  tin  ■   the  involute  of  the  teeth  of 

the   spiir-wlli-el. 

If  this  rale  i-  applied  b  t  ill  give 

curies  diffeti-  .Is. 

Ilv  taking  for  the  generating  curbs,  n-  in  the  Q 
o  B  and  o'  c,  sensibly  less  than   the  radii  of  the  pitch  eb 
inclination  of  the  common  tangent  to  the  Unejobb 

.  and  the  n  -nltin_'  form  of  tooth  possesses  greater  propot* 
width  and  strength  at  na  roots,  whbh  i-  ibelialile  for 
gearin  transmit  great  or  irregular  st. 

It  will  Ih-  observed  further,  that,  — "f^g  b  this  lystem,  tlm 

on  of  the  tlank   of  the  both 

indeed  the  curve  may  be  continued  down  b  th.-  line  ..f  the 
weh  with   a.|\  tooth  will,  in  I  '  •    much 

near  the  web,  whbh  is  n..t  the  nam 


BOOK   OF   INDUSTRIAL  DESIGN. 


teeth,  for  in  these  the  flanks  all  convergo  towards  the  centre  of  the 
wlurl,  and  the  tooth  is,  in  consequence,  narrower  at  the  neck,  close 
to  the  web,  than  at  tho  pitch  circle. 

Fig.  2  is  a  fully  shaded  elevation,  or  vertical  projection  of  the 
spur-wheel  separated  from  the  pinion.  The  portions  of  these 
wheels  not  particularly  referred  to,  are  constructed  on  tho  same 
general  principles  as  those  previously  discussed. 

helical    gearing. 

Figures  4  and  6. 

232.  If  to  a  worm-wheel  we  apply,  instead  of  a  worm,  a  pinion 
with  teeth  helically  inclined  to  correspond  to  the  similarly  inclined 
teeth  of  the  worm-wheel,  we  shall  have  a  spur-wheel  and  pinion 
constructed  on  the  helical  principle. 

This  svstem,  invented  in  the  seventeenth  century  by  Hooke, 
but  reprodifced  since  by  White  and  others,  claims  to  possess  two 
properties  which  have  been  often  thought  to  be  incompatible  with 
each  other — namely,  uniformity  of  angular  velocity,  and  freedom 
from  other  than  rolling  friction  between  the  teeth.  In  other  words, 
the  arcs  described  by  driver  and  follower  will  be  equal  in  equal 
times,  and  the  contact  between  the  teeth  will  resemble  that  of 
circles  rolling  on  planes. 

Added  to  these  properties,  and  consequent  to  them,  are  the 
advantages  of  a  constant  contact,  and  of  an  insusceptibility  to  the 
play  between  the  teeth,  which  invariably  exists  more  or  less 
palpably  in  gearing  constructed  according  to  the  systems  before 
described. 

The  form  of  the  helical  teeth,  as  taken  in  a  sectional  plane  at 
right  angles  to  the  axis  of  the  wheel,  may  be  derived  either  from  a 
couple  of  epicycloids,  or  a  couple  of  involutes  ;  it  is  only  the  sides 
which,  in  common  spur-gearing,  are  parallel  to  the  axis  that  here 
follow  the  inclination  of  a  succession  of  helices  coming  in  contact 
one  after  the  other.  The  arrangement  is  such  that  the  contact  of 
each  tooth  commences  at  one  side  of  the  wheel  and  crosses  over 
to  the  other,  and  does  not  cease  until  the  following  tooth  shall 
have  commenced  a  fresh  contact. 

The  helicoidal  system  may  be  applied  either  to  wheels  having 
their  axes  parallel,  as  spur-wheels,  or  intersecting,  as  bevil-wheels, 
or  again  inclined,  but  not  intersecting,  as  skew  bevils. 

In  figs.  4  and  5  are  represented,  in  face  and  edge  viow,  a  spur- 
wheel  and  pinion,  constructed  according  to  this  system  of  Hooke's, 
this  being  its  simplest  and  most  common  application : — Let  A  o  and 
a'  o  be  the  radii  of  the  respective  pitch  circles  of  the  two  wheels, 
these  radii  being,  of  course,  in  the  same  ratio  as  the  numbers  of 
the  teeth,  as  in  common  gearing.  The  radii  are  supposed  to  lie 
in  a  vertical  plane,  b'  c',  and  it  is  on  this  plane,  as  turned  at  right 
angles,  that  the  operations  represented  in  fig.  4  are  supposed  to  be 
performed. 

These  operations  have  for  then-  object  the  obtainment  of  the 
outline  of  the  teeth,  and  are  precisely  the  same  as  for  any  other 
epieycloidal  system  of  gearing.  Thus,  the  curves,  A  b  and  A  c, 
are  derive'd  from  the  generating  circles,  o  d  a  and  A  d'  o7,  as  also 
the  flanks,  A  d  and  a  e ;  but  it  is  unnecessary  to  repeat  a  detailed 
explanation  of  the  proceeding. 

Supposing,  then,  the  outline  of  the  teeth  to  be  drawn  as  on  the 


plane,  b'  c',  representing  say  the  anterior  face  or  base  of  the  wheels, 
next  draw  the  line,  E  f,  (fig.  5,)  representing  the  opposite  face,  and 
parallel  to  the  first,  limiting  also  the  breadth  of  the  wheels. 

To  proceed  methodically,  the  teeth  should  also  be  drawn  as  seen 
on  this  plane,  E  F  being  behind  the  outlines  of  the  anterior  ends  of 
the  teeth,  a  distance  equal  to  a  a',  or  rather  more  than  the  pitch. 
These  last  outlines  need  only  be  represented  in  faint  dotted  or 
pencil  lines  in  fig.  4,  as  the  parts  they  represent  are  not  actually 
seen  in  that  view  when  complete.  Thus,  starting  from  the  point, 
a',  on  the  pitch  circle  of  the  spur-wheel,  and  from  the  point,  g', 
on  the  pitch  circle  of  the  pinion,  wo  repeat  the  contours  of  tho 
teeth,  as  obtained  at  e  A  i  and  d  A  n,  respectively. 

As  the  result  of  this  disposition,  it  will  be  observed,  that  if  tho 
curve,  A  i,  of  the  tooth,  A,  of  the  spur-wheel  is  in  contact,  at  the 
pitch  circle,  with  the  flank,  g  d,  of  the  tooth,  g,  of  the  pinion  at 
the  anterior  face,  b'  c',  and  if  the  wheels  be  made  to  turn  to  a  cer- 
tain extent  in  the  direction  of  the  arrows,  the  curve,  a'  i',  on  the 
opposite  face,  E  F,  will  in  time  be  found  to  be  in  contact  with  tho 
corresponding  flank,  g'  d',  of  the  pinion.  In  other  words,  if  tho 
space  between  the  curves,  A  i  and  a'  i',  be  filled  up  by  a  helicoidal 
surface,  as  also  the  space  between  the  flanks,  g  d  and  ef  d',  all  the 
points  of  one'such  surface  will  be  in  contact  successively  with  the 
corresponding  points  on  the  other ;  so  that  when,  for  example,  the 
curve  a  V,  shall  have  reached  the  position,  A2  i3;  that  is,  when  it 
shall  have  passed  through  a  distance  equal  to  a  a',  the  posterior 
curve,  a'  i,  will  have  assumed  the  position  held  originally  by  a  i; 
or  rather,  a  position  directly  behind  this  in  the  plane  passing 
through  the  axis,  and  the  point  of  contact  between  a'  i'  and  a'  d' 
will  then  obviously  be  in  the  line  of  centres,  o  o'.  It  thus  follows, 
that  any  two  teeth  which  act  on  each  other  will  be  constantly  in 
contact  on  the  line  of  centres  throughout  a  space  equal  to  a  a'. 
This  space,  A  a',  is,  as  before  stated,  somewhat  greater  than  the 
pitch  of  the  teeth,  so  as  to  allow  a  following  couple  of  teeth  to  act 
on  each  other,  and  be  in  contact  on  the  line  of  centres  before  the 
eouple  in  advance  shall  bo  quite  free,  and  thus  a  constant  contact 
on  the  line  of  centres  is  preserved  throughout  the  entire  revolu- 
tion. 

In  order  to  delineate  the  lateral  projection,  fig.  5,  it  will  bo 
necessary  to  find  the  curves  which  form  the  outline  of  the  helicoidal 
surfaces  of  the  teeth.  The  principle,  according  to  which  this" is 
to  be  done,  is  precisely  what  has  already  been  explained  (208).  In 
the  present  case,  however,  as  we  have  but  fragments  of  helices  to 
draw,  in  place  of  finding  the  pitch  of  the  helix,  and  then  dividing 
it  and  the  circumference  proportionately,  it  will  be  sufficient  to 
divide  the  width,  b'  e,  of  the  wheels,  into  a  certain  number  of 
equal  parts ;  and  through  the  points  of  division,  to  draw  lines 
parallel  to  b'  c'.  Further,  the  arcs,  a  a',  e  e',  i  i',  must  be  divided 
into  a  like  number  of  equal  parts. 

To  render  the  diagram  clearer,  these  divisions  are  transferred 
to  1,2,  3,  4,  &c,  andl',  2',  3',4',&c.  (fig.  4.)  Each  point,  1,2,3,4, 
being  squared  over,  in  succession,  to  the  corresponding  lines  in 
fig.  5 — namely,  the  lines  of  division  first  obtained,  and  lying 
parallel  to  the  faces  of  the  wheels,  the  operation  will  give  the 
curve,  1,  3,  5,  6,  (fig.  5,)  corresponding  to  the  outline  of  the  exter- 
nal edge,  extending  from  i  to  i'.  The  curve,  I',  3',  5',  C,  similarly 
gives  the  other  edge.     It  is  also  obvious  that  the  line  of  junction 


af  the  tooth  »ith  tla*  web  "ill  be  represented  by  the  babY.- 

-  lb*  laet,  bat  lying  on 
liar  of  •  aoatewbat  afaallar  diameter. 

iteral  |-r. ;.«■!:  n.  of  all  the  teeth  are  determined  in  the 
mow  manner,  but  tat  ana,  aarame  various  aspect*, 

fr.<n  the  djfT.r.  ct  positions  in  which  they  lie  with  reapect  to  the 
iir'ki)  Bana* 

-  ruction,  in  order  to  determine  the  exact  inclination 

The 
■ 

■  nd  the 
i'  :  A  o  : :  ■'  I 

may  be 
oV...:,..l  _■■   ^n.  •-..:•. .  .imply  thu.  : — Maki    lln    straight    ;i;i, ,  m  >i. 
•  'jual  to  the  arc,  a  a'. 

lar,  I  L,  equal   :  ■'  E,  of 

the  wheel.  :  join  i   M.  *  iiulioD  of  the 

• 

•   ,  ial   to    the   ar. 
nationi,  L  I  au<J  I.  l.  (SUning 

Lh,  and  tin-  line,  c,  of  junction 
■     ■ 

■ 

lh,  with 
■  -.  difler- 
.  iiua  ia  amaller,  and  tbi  .  >rtional 

':  A  o*  ::■'■:  x. 

■ 

action, 

■.ill  pressure  n| 

.  of  the  nurl':. 

tudinal 

•  r  iho 

■     • 
■ 

of  a  m 

■ 

.   in   the 
■ 

*  of  tlio 
■ 

involute  and 

rtfaw  of 

i 

If  a  • 

i*   tra»i  lllng  along  a  curve, 


forma  of  the   respective  teeth   on  each  ah 
I   made   to   ti. 
glass  "  •  <:milar  to  lh..-  the  piston-rod 

attachm  parallel   motion,  and  also  exhibits! 

vibration  of  a  atrai^ht  wire,  a  how  breadth  i 
•.lined  in  this  manner 

•     that  whilst  according  to  Ihi 
rloidal  an.l  im  li  made 

up  of  1  •   natures,  whoa  .not,  in 

or  passage  trot 

preeiai-K  ■-  h-.ur- 

gtaaa  "  e  I  ntinuou*  ana' .  I 

any  way, 

-  of  the  same  | 

-  and  nicety  obtainal. 
• 

..rdinary  mail 
-  and  machinist  will  Dot  !«•  at  the   I 
• 

in.  tii- .•  i 

or  thin  board*  are  cut  to  ha 

llkh   U 

trial  with  a  |»air  of  com]«Kst-s,  a  centre  and  radii. - 
■ 

- 
trie  with  the  | 

■ 

'  ,-ira  ago 

iniinary 

■ 
another,  of  the 

I  in  the 

|  i 

calculati 

the  graduated  arale.  .  |  Ick  and 

■ 

■ 

■ 
•    ahould  be  ■, 


BOOK  OF   INDUSTRIAL  DESIGN. 


to  design  practical  arrangements  and  combinations  of  toothed  gear 
according  to  whichever  of  the  systems  may  be  preferred. 


CONTRIVANCES   FOR  OBTAINING   DIFFERENTIAL 
MOVEMENTS. 

THE    DELINEATION   OF   ECCENTRICS   AND   CAMS. 
PLATE    XXV. 

234.  Eccentrics  and  cams  are  employed  to  convert  motion, 
whilst  toothed-wheel  work  is  for  the  simple  transmission  of  it. 

Endued  themselves  with  a  continuous  circular  movement,  they 
are  so  constructed  as  to  give  to  what  they  act  upon,  an  alternate 
rectilinear  movement,  or  an  alternate  circular  movement,  as  the 
case  may  be,  the  motion  so  produced  being  obtainable  in  any 
desired  direction. 

CIRCULAR   ECCENTRIC. 

235.  There  are  several  descriptions  of  eccentrics.  The  simplest 
and  most  generally  employed,  consists  of  a  circular  disc,  completely 
filled  up,  or  open  and  with  arms,  according  to  its  size,  and  made  to 
turn  in  a  uniform  manner,  being  fixed  on  a  shaft  which  does  not 
pass  through  its  centre.  Such  eccentrics  are  represented  in 
Plate  XXXIX. 

The  stroke  of  such  a  piece  of  mechanism  is  always  equal  to 
twice  the  distance  of  its  centre  from  that  of  the  shaft  on  which  it 
turns ;  that  is  to  say,  to  the  diameter  of  the  circle  described  by  its 
centre  during  a  revolution  of  the  shaft.  The  motion  of  the  piece 
acted  upon  is  uninterrupted  during  either  back  or  forward  stroke, 
but  it  is  not  uniform  throughout  the  stroke,  although  that  of  the 
actuating  shaft  is  so ;  the  velocity,  in  fact,  increasing  during  the 
first  half  of  the  stroke,  and  decreasing  during  the  second  half. 

heart-shaped  cam. 
Figure  1. 

236.  When  it  is  required  to  produce  an  alternate  rectilinear 
motion  which  shall  bo  uniform  throughout  the  stroke,  the  shape  of 
the  eccentric  or  cam  is  no  longer  circular;  it  is  differentially 
curved,  and  its  outline  may  always  be  determined  geometrically 
when  the  length  of  the  stroke  is  known,  together  with  the  radius 
of  the  cam,  or  the  distance  of  its  centre  from  the  nearest  point  of 
contact. 

An  example  of  this  form  of  cam  is  represented  in  the  figure. 

Let  a  a'  be  the  rectilinear  distance  to  be  traversed,  and  o,  the 
centre  of  the  shaft  on  which  the  cam  is  fixed,  it  is  required  to 
make  the  point,  a,  advance  to  the  point,  a',  in  a  uniform  manner 
during  a  semi-revolution  of  the  shaft,  and  to  return  it  to  its  original 
position  in  the  same  manner  during  a  second  semi-revolution. 

With  the  centre,  o,  and  radii,  o  a,  and  o  a',  describe  a  couple  of 
circles,  and  divide  them  into  a  certain  number  of  equal  parts  by 
radii  passing  through  the  points,  1,  2,  3,  4,  &c.  '  Also  divide  the 
length,  a  a',  into  half  as  many  equal  parts  as  the  circles,  as  in  the 
points,  1',  2', '3',  &c.  Describe  circles  passing  through  these 
points,  and  concentric  with  the  first.  These  circles  will  succes- 
sively intersect  the  radii,  o  1,  o  2,  o  3,  &£.,  in  the  points,  h,  c,  d,  r, 
&c,  and  the  continuous  curve  passing  through  these  points  will 


he  the  theoretical  outlino  of  the  cam,  which  will  cause  the  point, 
a,  to  traverse  to  a',  in  a  uniform  manner,  for  the  equal  distances, 
a'  1',  1'  2',  2'  3',  &c,  passed  through  by  the  point,  a,  correspond 
in  succession  to  tho  equal  angular  spaces,  a'  1,  1 — 2,  2 — 3,  &c, 
passed  through  by  the  cam  during  its  rotation. 

As  it  is  not  possible  to  employ  a  mathematical  point  in  prac- 
tice, it  is  usually  replaced  by  a  friction  roller  of  the  radius,  o  i, 
which  has  its  centre  constantly  where  the  point  should  he  ;  and  it 
will  be  seen,  that  in  order  that  this  centre  may  be  made  to  travel 
along  the  path  already  determined,  it  will  be  necessary  to  modify 
the  cam,  and  this  is  done  in  tho  following  manner : — With  each  of 
the  points,  b,  c,  d,  &c.,  on  the  primitive  curve  as  a  centre,  describe 
a  series  of  arcs  of  the  radius,  a  i,  of  the  roller,  anil  draw  a  curve 
tangent  to  these,  and  such  curve  will  bo  the  actual  outline  to  be 
given  to  tho  cam,  B. 

It  will  be  seen  from  the  drawing,  that  tho  curve  is  symmetrical, 
with  reference  to  the  line,  a  e,  which  passes  through  its  centre; 
in  other  words,  the  first  half  which  pushes  (he  roller,  and  conse- 
quently tho  rod,  a,  to  the  end  of  which  the  roller  is  lilted,  from 
a  to  a',  is  precisely  the  same  as  tho  second  half,  with  which  the 
roller  keeps  in  contact  during  the  descent  of  the  rod  from  a'  to  a. 
Thus  the  regular  and  continuous  rotation  of  the  cam,  b,  produces 
a  uniform  alternate  movement  of  the  roller,  and  its  rod,  a,  which 
is  maintained  in  a  vertical  position  by  suitable  guides. 

In  actual  construction,  such  a  cam  is  made  open,  and  with  ono 
or  more  arms,  like  a  common  wheel,  or  filled  up,  and  consisting  of 
a  simple  disc,  according  to  its  dimensions ;  and  it  has  a  boss,  by 
means  of  which  it  is  fixed  on  the  shaft.  When  it.  is  made  open, 
it  is  cast  with  a  crown,  of  equal  thickness  all  round,  and  strength- 
ened by  an  internal  feather,  curved  into  the  boss  at  one  side,  and 
into  the  arm  or  arms  at  the  other. 

Examples  of  the  heart-shaped  cam  are  ,found  in  an  endless 
variety  of  machines,  and  particularly  in  spinning  machinery. 

cam  for  producing  a  tjniform  and  intermittent  movement. 
Figures  2  and  3. 

In  certain  machines,  as,  for  example,  in  looms  for  the  "  picking 
motion,"  cases  occur  where  it  is  necessary  to  produce  a  uniform 
rectilinear  and  alternate  motion,  but  with  a  pause  at  each  extremity 
of  the  stroke.  The  duration  of  the  pause  maj  he  equal  to,  oi 
greater,  or  less,  than  that  of  the  action.  Fig.  2  represents  tho 
plan  of  a  cam  designed  to  produce  a  movement  of  this  description; 
and  in  this  case  the  angular  space  passed  through  by  the  cam,  in 
making  the  point,  o,  traverse  to  the  position,  «',  is  supposed  to  bo 
equal  to  half  the  angular  space  described  by  it,  whilst  the  point.  ,;, 
is  stationary,  whether  in  its  position  nearest  to  the  centre,  or 
its  furthest,  a',  from  it.  For  this  reason,  the  circles  of  tho 
radii,  n  a,  and  o  a'  are  each  divided  into  six  equal  pints  in  tho 
points,  a',  1, /, g,  ft,  and  j.  Of  these  portions,  the  two  opposite, 
1  /'and  j  ft,  correspond  to  the  eccentric  curves,  h  j  and  I  It,  which 
produce  the  movement,  whilst  the  other  portions  correspond  to  tho 
pauses. 

After  having  drawn  the  diameters,  1  ft,  and  f  j,  the  eccentric 
curves,  ft  /',  anil  /  It,  are  determined  in  precise!)  the  same  manner 
as  tho  continuous  curve  already  discussed,  and  represented  in  fig. 
1.     That  is  to  say,  the  arcs  1  /,  and  j  ft,  are  to  be  divided  into  a 


M 


certain  Damber  of  f-qual  parts  by  radial  line.;  and  tho  1. 
-.-  onmbar  of  aqoal  parU  in 
■clee  are  to  be  drawn  through  the*, 
which  will  be  iatarneeted  in  the  point*,  c,  <L  r,  bt  the  radial 
liaea.     Lines  paeaiaa;  through  theee  point*  of  intersection  a 
•  sought,  »/.  and  I  a. 
The  in,  eat  and  f  g  a,  which   unite   tl 

era  concentric  with  the  abaft,  and  conaeque 
the  point  remain*  to  contact  with  these  an-  I   with- 

out  motion,  aJ 

of  a  ca-v  the  one,  c,  ui>!>  r  I — that 

derived 

from  tli' 

mathematical  p  >n  is  fully  indicated  - 

a  !»•«• ,  i»  made  \  • 

cut  awav,  and 

crown,  anna,  and  a  gnat   part   of  the  boat  ill  of  a 

tK»fc»».»l  aa  will  be  more  plainly  aMB  iti  i 

I 
■iodic. 

-    • 

ns  In  which  they  are  ctetennmad  an 

-     lis  of  the  an1, 
which  takes  the  place  of  the  straight  lino,  a  <r\ 

TIUISVUI     CAM. 
I-*    \    AXD    5. 

■  of  a  curvilinear  equilateral 

• 

rrcumgular  form,  a*  at  T,  fig*.  A  and  IS-     It   ii    hollowed   out  in 

planed  edges,  to  a  surface,  a  b,  on  tin'  cylinder,  i>.  also 
true,  n'i  ;  Ita  I  m.te.n  is  I"  allow  ii .. 

to  pass  alternate.)  to  ih.-  nffjar  pari  of  the  cylinder,  by  the  |»>rt, 

■ 
the  ts. 

i.tuaN-d  wllli  nn  alter- 

.  attached   to  a  vertical   rod,    I 

the  Tall  1   in  ti";. 

©.  and   ■ 
which  •  am,  o. 

of  tlie  valve  a  certain  distance  and  intomiitti  ntly,  in  sm-h  a  man- 
ner that   the    | 
•team  for  a  certain  til 

■     which    it    traverses;    with  .   and    with    this 


ii!*lTrr».  o  a,  for  a  radius,  describe  a   i  into  six 

equal  pacta,  in  ll 

ita,  aa  I  and  '2,  and  with  Die  same  ra 
area,  o  'J,  and  ■  l  I  unilinear  Irian;;!.',  ..—  1 — 2, 

■ 

the  parallels,  i — I  and  4 — A,  tangential  to  the  two  sides 

of  the  !r..i:-._!. .  o,  and  we  -Kail  thus  obtain   the   uj.|«  r  and 

M  th*  two  aides  of  the  frame, 
I' 

abaft,  J,  as  shown  in  I 

■hat  if  I  lie  shaft   lur:. 
■ 
the  upj-  will  cause  i:  I 

■ 

l 
lion,  m  n.  then  hv  tod 

ance  equal  to  i. 
d.  ii  umo.ered.  so  as  to  allow 
of  tlie  oyundc*  (fig.  B);  whiUt.  on  the  oil,.  .  :mnica- 

.ind  the  aaampi 

E,  so  th  .  D  |iai.s  out  from  the  upper  end  of  th 

dor.     Li  the  moTomenl  of  tbi    ■ 
■tab.  of  a  revolution,  I 

Me  with  tlie  avis,  dooa 
not  chat  frame,  as  lot 

with  it-  ■  al  MOB,  bowOTOr,  M   t 

1,  will   ba  in  i: 
and  it  will,  in  ■  ■  tact  with  the  lower 

h  i-  in   tin-  position  of  the  horizontal  cent 
3 — i.    Tin-  further  revolution  of  t 

from  ita  pressure  on  the  lower  side,  until  tl 
0  I,  "I    I 

the  tana  will  occupy  the  position,  m'  «'.  i  to  lha 

tad  in  tig.  3. 
It    follow-,   from    toil   arra-  remain 

\  when  it  arr  and  the 

pause  each  time  will 

rotation  of  the  i-atii  abaft     'Hie   n|  Miwanl 

.  tring  a  third  •■:  and  tho 

.  ,11  not  !»•  unifonn.  although  the  r..: 

In  actual  construction,  the  angles  of  tin' 

I    to   avoid   a    too    -ud.lin   change  of 

•  •  frame. 

C  A  M. 

i-    |     AM.    7. 

In  certain  industrial  arts,  an  instrument   b 
poundin 
tnnl.ark.  for  evani|.le.  in  which  the  •  : 

■  through 
.   a   well 
known  working  application  of  this  ei: 


BOOK   OF   INDUSTRIAL   DESIGN. 


la  these  cases,  the  stamp,  or  hammer,  lias  to  be  raised  or  tilted 
up  preparatory  to  each  succeeding  stroke,  and  it  is  obvious  that 
this  may  be  most  economically  done  in  a  gradual  manner.  It  is 
generally  effected  by  a  cam,  the  outline  of  which  is  the  involute 
curve  already  described  ;  this  form  being  preferable  on  account  of 
tne  uniformity  of  its  action. 

The  office,  then,  which  the  cam  under  consideration  has  to 
fultil,  is  the  raising  of  the  stamp,  or  load,  to  a  certain  height,  and 
then  the  letting  it  fall,  without  impediment,  upon  the  object  sub- 
mitted to  its  action. 

The  diameter  of  the  cam-shaft  being  predetermined,  as  well  as 
that  of  the  generating  circle,  which  last  is  usually  the  same  as  that 
of  the  boss  of  the  cam,  the  design  is  proceeded  with  as  follows : — 
Letting  A  be  the  cam-shaft,  and  taking  A  o  as  the  radius  of  the 
generating  circle,  whilst  a  a!  is  the  height  to  which  the  projection, 
B,  fig.  03,  formed  on  the  stamp,  c,  is  to  be  raised,  develop  the 
circumference  (197)  of  the  circle  of  the  radius,  A  o,  by  means 
of  a  series  of  tangents  which  give  the  points,  c,  d,  e,  &c,  the  curve 
passing  through  which  forms  the  involute,  bfi.  The  inner  por- 
tion, b  o,  is  not  a  continuation  of  the  involute,  but  simply  joins  the 
boss  with  a  circular  turn,  because  the  stamp  projection,  B,  does 
not  approach  the  cam-shaft,  a,  nearer  than  the  point,  a,  to  which 
b  corresponds.  Through  the  point,  a,  draw  the  vertical,  a  a',  and 
make  it  equal  to  the  height  to  which  the  stamp  has  to  be  raised ; 
then  with  the  centre,  A,  and  a  radius  equal  to  a  a',  describe  the 
arc,  a'  m  i,  which  will  cut  the  involute  in  the  point,  i,  and  this 
point  is  consequently  the  outer  limit  of  the  cam.  A  little  con- 
sideration will  show  that  if  the  cam-shaft,  a,  be  turned  in  the 
direction  of  the  arrow,  supposing  that  it  is  originally  placed,  so 
that  the  point  b,  coincides  with  a,  it  must  necessarily  raise  the 
lifting-piece,  b,  the  lower  side  of  which  is  indicated  by  the  line, 
m  ft,  and  wall  carry  it  by  equal  increments  up  to  the  position,  m'  a'. 
The  point,  i',  will  then  have  attained  the  position,  a1,  and  the  rota- 
tion continuing,  the  next  moment  it  will  pass  it,  when  the  cam  will 
be  entirely  clear  of  the  lifting-piece,  B,  and  this  last  being  unsup- 
ported, must  fall  by  its  own  weight. 

The  involute  might  have  been  derived  from  a  generating  circle 
of  the  radius,  a  a,  and  had  this  radius  been  adopted,  the  resulting 
curve  would  have  been  shorter,  notwithstanding  that  it  would  give 
the  same  extent  of  lift.  The  angular  space  passed  over  would 
also  be  less,  and  this  would  admit  of  a  higher  velocity  of  the  cam- 
shaft, and  the  strokes  might  be  given  in  more  rapid  succession, 
whilst  on  the  other  hand,  a  greater  power  would  be  required  to 
raise  the  same  weight. 

The  cam  we  have  represented  in  fig.  |B),  is  such  as  is  employed 
to  actuate  the  chopping  stamp  of  mills  for  reducing  oak,  or  other 
bark,  for  the  preparation  of  tan.  The  bark  is  placed  in  a  land  of 
wooden  trough,  e,  solidly  fixed  into  the  floor.  The  stamps  are 
armed  with  a  series  of  cutters,  n,  in  the  form  of  crosses.  The  side 
of  the  trough  next  to  the  stamp  is  vertical,  whilst  the  opposite  side 
is  elliptical  in  shape,  and  the  matter  under  operation  has,  con- 
sequently, always  a  tendency  to  fall  under  the  stamp.  The  stamps 
are  kept  vertical  bv  slides  in  which  they  work.  They  are  generally 
from  450  to  700  pounds  weight,  and  fall  through  a  height  of  from 
16  to  20  inches. 

Fig   7  is  a  plan  of  the   cam  as  seen   from  below,  and  fully 


indicates  the  width  of  the  rim,  and  of  the  boss,  and   the   thickness 
of  the  feather  or  disc  uniting  the  two. 

A  series  of  such  cams  are  frequently  employed  in  different 
planes  on  the  same  shall,  actuating  a  corresponding  scries  ..(' 
stamps,  and  in  such  ease  they  are  arranged  in  steps  so  as  to  come 
into  action  one  after  the  other.  Two  or  more  are  also  sometimes 
employed  in  the  same  plane,  and  working  a  single  stamp.  In  this 
latter  case,  the  generating  circle  requires  to  bo  of  much  larger 
diameter  in  proportion,  but  the  principle  of  construction  is  how- 
ever the  same. 

CAM   TO   PRODUCE    INTERMITTENT   AND   DISSIMILAR    MOVEMENTS. 
FlUUKES    8    AND    9. 

240.  In  certain 'examples  of  steam  engines,  the  valve  movement 
is  obtained  from  a  species  of  duplex  cam,  which  being  formed  of 
two  distinct  thicknesses,  affords  a  means  of  adjustment  whereby 
the  valve  may  be  made  to  move  intermittently  and  at  different 
rates,  the  proportions  of  which  are  variable  at  pleasure.  Tho 
object  of  this  is  to  form  and  shut  oft'  tho  communication  between 
the  cylinder  with  the  steam-pipe,  at  any  required  point  of  tho 
stroke.  In  other  words,  the  arrangement  permits  of  the  winking 
of  the  machine  on  the  expansive  principle,  and  of  varying  the 
"cut-oft'"  point  at  pleasure  within  certain  limits.  We  shall  see, 
at  a  more  advanced  period,  what  is  to  be  understood  by  the  fore- 
going expressions.  In  designing  cams  of  this  class,  we  primarily 
determine  the  radius  o  a,  of  the  cam  boss,  and  the  entire  length] 
b  c,  of  the  stroke  to  be  given  to  the  valve-rod.  This  distance, 
which  in  the  present  instance  we  shall  take  as  equal  to  three  limes 
the  height  of  the  port,  must  not  be  traversed  at  one  movement 
On  tho  contrary,  a  third  only  of  this  is  at  first  passed  111 
with  some  rapidity,  and  the  remaining  two-thirds  are  traversed  at 
a  later  period,  in  a  continuous  manner:  in  other  words,  after  a 
third  of  the  stroke  lias  been  traversed,  a  slight  pause  takes  place 
before  the  remainder  is  traversed,  and  a  second  pause  also  occurs 
before  the  commencement  of  the  return  stroke. 

After  describing  a  couple  of  concentric  circles  with  the  respec- 
tive radii,  o  a,  and  o  c,  and  having  determined  the  angular  spaces, 
a  d,  and  f  g,  corresponding  to  the  times  during  which  the  valve  is 
to  remain  stationary,  and  the  spaces,  o-  h,  and  c/,  corresponding  to 
the  duration  of  the  movements;  divide  the  whole  Stroke,  ' 
three  equal  parts  in  the  points,  i,j,  through  which  descril  e 
concentric  with  tho  preceding.  Through  the  points,/,  »-,  h,  draw- 
radii,  and  produce  them  to/",  g',  and  /;'. 

As  the  cam  will  act  on  two  friction  rollers,  g,  diametrically 
opposite  to  each  other,  their  radius  is  determined,  as  a  e  ;  one  is 
drawn  with  its  centre,  e,  on  the  radius,  o  a  produced,  and  tangen- 
tial to  the  circle  described  with  that  radius:  the  other,  with  its 
centre,  e ,  on  the  radius,  o  c  produced,  is,  in  like  manner,  tangential 
to  the  circle  described  with  this  radius. 

Between  the  two  points,  d  and  k,  and  comprised  within  tho 
given  angle,  g  o  h,  a  curve.  /.  /  </.  is  drawn  and  united  by  tangential 
arcs  at  either  extremity  with  the  circles  of  the  radii,  a  <i  and  o  i, 
respectively,  in  such  a  manner  as  to  avoid  any  sudden  change  of 
direction.  Next  divide  the  arc,  g  h,  into  a  certain  number  of  equal 
parts  in  the  points,  1,  2,  &c.,  and  carry  the  radii  across  to  1',  3, 
&c. ;   then,  on  each  of  these  radii,  as  a  centre  line,  describe  an  arc 


T1IK    I 


'  to  the  radio*  of  the  roller,  o,  and  tangential  to  the 

bl   obtained  the  pointa.  r  t  t, 

indicating  the  MKceeaive  poaitiaaa  of  the  centre  of  the  roller  on 

the  foe,  e  r*.  when  impelled  I  -tailing 

from  these  aeveral  pointa,  we  meaaure  on  the  corresponding  croea 

.  frifiy  equal  to  I  - 

-    .« .-  ahaD  obtaia  the  poaitiona,  r,  r*.  I ,  of  l)  - 

•     •      -.      '-.■•■■       'I 
time  poiata,  r,  a,  I.  m 

.J  to  them,  and  unite 
the  radii,  c  o  uxij  a,  in  a  aunilar  DM 
■ 

-t,  i  I  It, 

In    w  may  maintain 

the  M 

- 
lira.!-.  the  ram  and  an  '  planed 

!'  the  frame  is  bolted  the  cast-iron  • 
I 
on  the  centre  u.  and 

.  ••■  T.  fig.  B.  above.     In  th.   : 
•    the  ram  and  r.>!l.-r  frame,  in  fig.  S,  the  fltfi 

•    |«rt,  <r\  and    this   remains   ojx-n  whilst    I 
arc,  a  A,  and  Etl 
mi  shaft,  o. 
/.  shall  have  arrival  at  the  | 

■     ■ 
v  pass  thmu^h  th<-  anLnV.  J  o  g,  and 

r 

• 

•  will,  in 
fact,  be 

V 

- 1 1  •  .rt  time,  during  which  1 1 ,  - 

in,  hew. 

actuating  gear,  will  :i.  intil  the 

open.     'lliis  mov<  men!  will  tal 

i   >>y  the 
-.  ■;.  and  th'-  frame  >tiil  farther 
n  to  the 
■  and  o  r,  in  the  Mime  manner  at  t!i 

.  a  in  n, 
i*  ubla 

•  ire  fully 

in,  and  it  baa  in  mind 

that  th<  -.ict  with 

hi  haa   paw. 

iry  during  an 
Umawaad,  and   then  If* 
nwnre  to  art  iij«.d  the  roller,  o\  and  cause  it,  with  the  frame,  to 


return  from  right  to  left,  and  the  movemente  and  inter  \a)s  will  take 

iii)  it  ree/hta 

rt-aperta,  and  laid  u|- 

aa  m  attd 

■ 

that  half  of  the  cam  » 

a.,  that. 

• 

manner  ia  obtained  a  i  rate  of  expat 

which  ll 

t  m'.  of 
■ 

.  it  i. 

An  innumi  r:  I  by  the 


RULES   AND  PRACTICAL  DATA 

•j ll    T  • .  during 

•■!  draw 

a  force 
upon   n  ■  1   t.i   it.  and 

continui 

It  followa  from 
tlint  the 
two  in-! 

passed    through    in    a    given    time,  or    the 

Tin-  amount  of  mechanical  work  increase*  directly  as  the  increase 

i  ..f  the 
■ 

■ 
»..rk  m  1x1=4.     II 

dan;   and  if,  with   the 

- 

well—-  16,  or 

il  amount. 

In  th.  f  "8  that.  !n  fact 

just  a-  - 


LOOK   OF   INDUSTRIAL   DESIGN. 


length,  breadth,  and  depth,  so  also  is  mechanical  effect  defined  by 
the  three  terms  representing  pressure,  distance,  and  time.  This 
analogy  gives  rise  to  the  possibility  of  treating  many  questions 
and  problems,  relating  to  mechanical  effects,  by  means  of  geometri- 
iul  diagrams  and  theorems. 

The  unit  of  mechanical  effect  (corresponding  to  the  geometrical 
cubical  unit)  adopted  in  England,  is  the  horse  power,  winch  is 
equal  to  33,000  lbs.  weight,  or  pressure,  raised  or  moved  through 
a  space  of  1  foot  in  a  minute  of  time.  The  corresponding  unit 
employed  in  France  is  the  kilograuimetre,  which  is  equal  to  a 
kilogramme,  raised  one  metre  high  In  a  second.  Thus,  supposing 
the  pressure  exerted  be  20  kilog.,  and  the  distanco  traversed  by 
the  point  of  application  be  2  metres  in  a  second,  the  mechanical 
effect  is  represented  by  40  k.  m. ;  that  is,  40  kilog.,  raised  1  metro 
high.  This  unit  is  much  more  convenient  than  the  English  one, 
from  its  lesser  magnitude.  Indeed,  when  small  amounts  of  me- 
chanical effect  are  spoken  of  in  English  terms,  it  is  generally  said 
that  they  are  equal  to  so  many  pounds  raised  so  many  feet  high. 
That  is  to  say,  this  takes  place  in  some  given  time,  as  a  minute, 
for  example.  The  time  must  always  be  expressed  or  understood. 
It  is  impossible  to  express  or  state  intelligibly  an  amount  of 
mechanical  effect,  without  indicating  all  the  three  terms — pressure, 
distance,  and  time.  It  is  to  the  losing  sight  of  this  indispensable 
defiuition,  that  we  may  attribute  the  vagueness  and  unintelligibility 


of  many  treatises  on  this  subject    Tlio  French  engineers  make 

the  horse  power  equal  to  75  kilogramme  ties  ;  thai  is,  to  7.0  kilog., 
raised  one  metre  high  per  second. 

The  motors  generally  employed  in  manufactures  and  industrial 
arts  are  of  two  kinds — living,  as  men  and  animals  ;  and  inanimate, 
as  air,  water,  gas,  and  steam. 

The  latter  class,  being  subject  only  to  mechanical  laws,  can 
continue  their  action  without  limit.  This  is  not  the  case  with 
the  first,  which  are  susceptible  of  fatigue,  after  acting  for  a  certain 
length  of  time,  or  duration  of  exertion,  and  require  refreshment 
and  repose. 

Wliat  may  be  termed  the  amount  of  a  day's  work,  producible 
by  men  and  animals,  is  the  product  of  the  force  exerted,  multiplied 
into  the  distance  or  space  passed  over,  and  the  time  during  which 
the  action  is  sustained.  There  will,  however,  in  all  cases,  be  a 
certain  proportion  of  effort,  in  relation  to  the  velocity  and  duration 
which  will  yield  tho  largest  possible  product,  or  day's  work,  for 
any  one  individual,  and  this  product  may  be  termed  the  maximum 
effect.  In  other  words,  a  man  will  produce  a  greater  mechanical 
effect  by  exerting  a  certain  effort,  at  a  certain  velocity,  than  he 
will  by  exerting  a  greater  effort  at  a  less  velocity,  or  a  less  effort 
at  a  greater  velocity,  and  the  proportion  of  effort  and  velocity 
which  will  yield  the  maximum  effect  is  different  in  different 
individuals. 


TABLE    OF    THE    AVERAGE    AMOUNT   OF    MECHANICAL   EFFECT   PF.ODUCIELE    BY   MEN   AND    ANIMALS. 


A  man  ascending  a  slight  incline,  or  a  stair,  without  a  burden,  his  work 

consisting  simply  in  the  elevation  of  his  own  weight, 

A  labourer  elevating  a  weight  by  means  of  a  cord  and  pulley,  tho  cord 

being  pulled  downwards, 

A  labourer  elevating  a  weight  directly,  with  a  cord,  or  by  the  hand,. 
A  labourer  lifting  or  carrying  a  weight  on  his  back,  up  a  slight  incline,  or 

stair,  and  returning  unladen, 

A  labourer  carrying  materials  in  a  wheel-barrow,  up  an  incline  of  1  in  1: 

and  returning  unladen, 

A  labourer  raising  earth  with  a  spade  to  a  mean  height  of  five  feet,. . . 

ACTION    ON    MACHINES. 

A  labourer  acting  on  a  spoke-wheel,  or  inside  a  large  drum. 

At  the  level  of  the  axis, 

Near  the  bottom  of  the  wheel, 

A  labourer  pushing  or  pulling  horizontally, 

A  labourer  working  at  a  winch  handle, 

A  labourer  pushing  and  pulling  alternately  in  a  vertical  direction,. . . . 

A  horse  drawing  a  carriage  at  an  ordinary  pace, 

A  horse  turning  a  mill  at  an  ordinary  pace, 

A  horse  turning  a  mill  at  a  trot 

An  ox  doing  the  same  at  an  ordinary  pace, 

A  mule  do.  do.  

^n  ass  do.  do.  


143 

40 
44 

143 

132 


132 

•50 

26 

2-30 

26 

1-97 

Hi 

3-46 

11 

361 

154 

2-95 

90 

3-96 

66 

6-56 

1  13 

197 

66 

2-95 

31 

262 

1  tout  hi-h. 

715 


26-0 
246 


8-5 

7-8 


660 
59-8 
512 
430 
39-7 
454-3 

•JIlL'-O 

4330 
281-7 
194-7 
81-2 


8 
10 
8 
4i 


I 


561,600 
531,360 


401,760 


306,000 

2S0.00O 


1,900,800 

I.T-Jl'.-JIO 
1,474,560 
1,238,400 
I.I  I.:  360 
16,354,800 

7,01  1,600 
S.I  12,960 

2,338,560 


It  may  be  gathered  from  this  table  that  a  labourer  turning  a 
winch  handle  can  make  its  extremity  pass  through  a  distance  of 
2-46  feet  per  second,  or  60  x  2-46  =  147-6  feet  per  minute. 
Then,  supposing  the  handle  has  133  inches,  =  1-147  feet  radius, 
which  corresponds  to  a  enrnnjference  of  6-28  x  1-147  =  72  feet 


at  the  point  of  application,  the  labourer  is  capable  of  an  average 
velocity  of 

■ =  20  turns  (nearly)  per  minute. 

Also,  the  same  labourer  exerting  a  force  equal  to   17J  lbs.  with 


■I 


TIIK    1 


ftaft  par  second,  will  produce  a  mechanical 
•fleet  equal  to 

ha  raiM>d  I  foot  high  per  second,  or  of 
43  x  60  =       2580  |- 

858"  hour. 

And  a*  he  cm  work  at  this  b  I  \nnical 

be,  as'  indicated  in    Uie   table,  equal 
-  tOO  Iba.  raised  1  foot 
W.     may    then   calculate   Out,   aa  a   day's   work,  a   I 

a  » inch-hand  ■  ..inner  17J  \\n. 

par  aooond;  wbj  Iba  labonraf  lias  only 

to  api  to  a  crane,  a  windlass,  or  a 

capstan,  he  can  develop  a  m 

. 
crane,  a  man  can  in  90'  raise  a  load  of  10480  lbs.  to  ■  !, 
npan  this  with  die  tabuL 

pounds  raised 
1  foot  high  in  a  ageood,  to  which  tl,.  |  jnal. 

It  bai  i    by  experiments,  that  mdar  the  moat 

favourable  cm-..- 

•   exertion,  raise  to   the  same  height,  1CJ  : 

h  is  equal  to  a  mechanical  • :' 

1474  x  1W  „        .     ,     . 

J.'j  lbs.  raised  1  tool  Ugh  \*-r  - 

A  man  can  evidently  only  axerl  itwfa  a  force  daring 
lin.it. -1  |  kind  of  labour 

with    tliat   which    eoBl  hours. 

■  the  l..ail  in.. I  velocity  as  given  in  the  table  are  those 
h  oil.,  r.  still,  when  U 
requires  it,  they  might  l>o  altered  I  '  .  thus,  if  it  is 

neccsaary   to   apply  I  In ■u.iiy  of  the 

winch-handle  i  it]   w..uM   be   i 

and  would  become 
43 

:    3    16. 

35 

It  ha-  1  from  actual  obeervationa,  thai  a  horse, 

going  at  the  n  •  r  hour, 

cannot    exert    a   greater   UetlUft    forea    than    the   OOrroapundlng 

draw  anything 

appreciable  when  going  at  the  rate  of  16  miles  |*r  hour. 

Thus,  when  it  ■  warned  to  ineraua  the  i 
takes  place  in  the  veloertj  ;  an. I  reciprocally,  when  it  i- 
to  gain  time  ami  apeed,  it  ran  only  ba  done  at  the  expense  of  the 
load.    'Pin-,  in  the  eaae  of  the  winch-handle,  the  two  tnetore 
must  ahrayi  produea 

'her. 
In  al! 
impressed,  for  without  mumnnit  there  con!. I  DO)  I- 
I  '..r.  • 

-  ..f  motion — uniform.  I  on, 

I   ■    niiifonii 

ii  equal  times. 
TVon,  f.>r  example,  if  a  body  b 

('  "  n  is  iiml'oriii.      | 


i  T  the 
.mee  is 
equal  to  I 

Firit   Example. — T 

h  what  distance  will   it  liavo 

D  =  3  x  15  =  4S 

I) 


From  the  preceding  formula,  D  =  V  x  T,  is  obi. 

that  is  '  :  .1  is  equal  to  the  distance 

■ 
/       -fir. — Tin'  distance  passed  through  in  13 

45 
V=,6=;' 

machinery,  as  well  as  mar 
.-,  for  the  most  |Mrt,  actuated  in  a  uiiilorm 

•J  II.   Vakiip   IfoTKML — Wh.n    a   body  pass,.*   in    equal  timi-s 

through  ii  augment  or  deereaae  by  equal  qui 

Uie  motion  is  called  uniform!* 

The  distance  in  motion  uniform' .  ..d   to  half  the 

.sum  of  the  extreme  v<  locitiea  multiplied  b]  the  time  in  »• 

First    I  What    is    the    d  I    through    in   4 

by  a  body  in  motion,  the  velocity  of  whiel 

second  at  starting,  and  '. 

3  +  6 
D  =  -^     x  4=  l 

/  V.  |«ss4sl   thr.o 

by  a  body  in  motion,  which 

I.  ft  .  t  per  sjeond,  hut  which  is  gradually  red  i. 


D  = 


x  4  =  1 


It  will  1m>  seen  from  thee*  two  axamplea,  that,  with  like  i di 

tions,  th,.  total  ilisiance  la  the  s;iiiie  for  notiona  onifohx 
-  !■  i. 
The  velootty  at  the  tod  of  a  given  time,  in  uniform)} 

DOB,  is  equal   to  the  Velocity  at   starting,  plus  tin-   prodooj 
of  the  ii.  'id  into  the  time  in  s,c..n.ls. 

/        /         ...— \\  hat  reloelty  will  a  body  have  at  th. 

the  initial  Velocity  —  I,  and  that   it   il 
at  the  rate  ot                               lid  ? 

V  =  1  +  (8  x  3)  =  . 

The  Velocity  which,  at  the  .  'iiiica  body  uniformly 

:    should  ban  Ity   minus   the 

produol  of  the  dimiiiu  1*0  the  tune   in 

/       .jir  —  \  bod]  in  noi 

m.i,  and  ii-  reloeHj  docreenea  at  tit 
•  nil,  what  will  !-■  the  velocity  at  the  end  oi  I 
V  =  23  —  (3  x  10)  =  a  i 
r  which  the  varloni  | 
two  prtneipal  kinds — oontinuoua,  mid  alt. 
ad  forward  mot 


BOOK  OF  INDUSTRIAL  DESIGN. 


These  two  kinds  of  motion  may  take  place  either  in  straight  or 
curved  lines,  the  latter  generally  being  circular. 

In  the  actual  construction  of  machinery,  wo  find  that,  from 
these  principal  descriptions  of  motions,  the  following  combinations 
are  derived : — 

t  Continuous  rectilinear. 
Continuous  rectilinear  motion  is  converted  into  }  Continuous  circular. 

t  Alternate  circular. 

r  Continuous  rectilinear. 
Alternate  rectilinear  motion  is  converted  into     \  Continuous  circular. 

<  Alternate  circular. 

r  Continuous  rectilinear. 
«     ..  ,  .    ,  ■    .  I  Alternate  rectilinear. 

Continuous  circular  motion  is  converted  into      4  Continuous  circular 

I  Alternate  circular. 


Alternate  circular  motion  is  converted  i 


'  Alternate  rectilinea 
.  Alternate  circular. 


THE    SIMPLE    MACHINES. 

246.  This  term  is  applied  to  those  mechanical  agents  which 
enter  as  elements  into  the  composition  of  all  machinery,  whether 
their  function  be  to  elevate  loads,  or  to  overcome  resistances. 

The  simple  machines  are  generally  considered  to  be  six — the 
lever,  the  wheel  and  axle,  the  pulley,  the  inclined  plane,  the 
screw,  and  the  wedge. 

A  much  more  scientific  and  comprehensive  arrangement  of  the 
elementary  machines  is  (hat  lately  suggested  by  Mr.  G.  P.  Ren-, 
shaw,  C.E.,  of  Nottingham.  According  to  his  system,  the  elemen- 
tary machines,  or  mechanical  powers,  are  five — namely,  the  lever, 
the  incline,  the  toggle  or  knee-joint,  the  pulley,  and  the  ram. 

The  wheel  and  axle,  of  the  first  system,  is  evidently  but  a 
modification  of  the  lever,  and  the  screw  and  wedge  are  modifi- 
cations of  the  inclined  plane  ;  whilst  no  mention  is  made  of  the 
toggle-joint  and  ram — the  last  so  well  represented  by  the  hydro- 
static press. 

All  these  machines  act  on  the  fundamental  principle,  known  as 
that  of  virtual  velocities.  According  to  this  principle,  the  pressure 
or  resistance  is  inversely  as  the  velocity  or  space  passed  through, 
or  that  would  be  passed  through,  if  the  piece  were  put  in  motion. 
The  momentum  of  the  power  and  resistance  is  equal  when  the 
machine  is  in  equililtrio.  By  momentum  Is  understood  the  pro- 
duct of  the  power  by  the  space  passed  through  by  the  point  of 
application. 

Time  is  occupied  in  the  transmission  of  all  mechanical  force. 
In  any  mechanical  action  we  do  not  see  the  effect  and  the  cause 
at  the  same  instant.  Thus,  in  continuous  motion,  in  which  the 
time  expended  is  not  apparent  at  first  sight,  each  succeeding  por- 
tion of  the  motion  is  due  to  a  portion  of  tho  impelling  action 
exerted  a  certain  time  previously.  This  will  bo  moro  obvious  on 
observing  the  commencement  and  termination  of  any  motion. 
The  motion  does  not  commence  at  the  instant  that  the  power  is 
applied,  nor  does  it  cease  at  the  exact  moment  of  the  power's 
cessation.  The  fiction  of  the  vis  inertia;  has  been  invented  to 
account  for  these  latter  observed  facts,  but  it  explains  them  very 
awkwardly.  Thus,  bodies  are  said  to  possess  a  certain  force 
■  which  is  opposed  to  a  change  of  state,  whether  from  rest  to  motion 
or  motion  to  rest.  If  such  a  resistive  force  existed,  it  would 
require  an  effort  to  overcome  it,  in  addition  to  what  is  actually 


accounted  for  by  the  motion.  If  it  is  said  that  this  is  again  given 
back  at  the  termination  of  tlio  motion,  another  fiction  is  required 
to  account  for  it  in  tho  meantime,  that  is,  during  tho  continuation 
of  the  motion.  Moreover,  there  is  nothing  analogous  to  it 
throughout  tho  ontiro  range  of  physical  science. 

The  facts  are  described  in  a  much  more  simplo  and  philosophi- 
cal manner,  when  they  are  said  to  arise  from  tho  lime  taken  in  the 
transmission  of  motive  force.  Why  thero  should  bo  this  expen- 
diture of  time  is  a  more  abstruse  question.  It  probably  arises 
from  tho  elasticity  of  the  component  particles  of  bodies  and 
resisting  media,  and  is  regulated  by  the  laws  which  govern  the 
relation  to  time  of  the  vibrations  of  tho  pendulum. 

In  all  machines,  a  portion  of  tho  actuating  power  is  lost  or 
misapplied  in  overcoming  the  friction  of  the  parts. . 

247.  The  Lever. — Tho  lever,  in  its  simplest  form,  is  an 
inflexible  bar,  capable  of  oscillation  about  a  fixed  centre,  termed 
the  fulcrum.  A  lever  transmits  the  action  of  a  power  and  a 
resistance,  or  load;  the  distance  of  the  power,  or  load,  from  tho 
centre  of  oscillation,  is  called  an  arm  of  the  lever. 

There  are  two  kinds  of  power  lovers,  distinguished  by  tho  posi- 
tion of  the  fulcrum  as  regards  the  power  and  the  resistance. 
These  become  speed  levers,  by  transposing  the  power  and  resist- 
ance. By  a  potter  machine,  is  meant  one  which  gives  an  increase 
of  power  at  the  expense  of  speed,  and  by  a  speed  machine,  ono 
that  gives  an  increase  of  speed  at  the  expense  of  power,  and  .ill 
tho  simple  machines  are  one  or  the  other,  according  to  the  relative 
position  of  the  power  and  resistance. 

In  all  cases  of  the  lever,  the  ■power  und  lie  resistance  are  in  the 
inverse  ratio  to  each  other  of  their  distances  from  the  em/re  qfoseil- 
lation.  That  is  to  say,  that  when,  in  equilibria,  the  momentum 
of  tho  power,  P  X  A,  or  the  product  of  this  power  into  the  space 
described  by  the  lever  ami,  A,  is  equal  to  the  product,  R  x  B,  of 
the  resistance,  into  the  space  described  by  the  lever  arm,  B  :  whence 
the  following  inverse  propoi  tioii : — 

P  :  R  ::  B  :  A; 

Any  three  of  which  terms  being  known,  the  fourth  can  he  found 
at  once. 

248.  The  wheel  and  axle  is  a  perpetual  lever.  As  a  power,  the 
advantage  gained  is  in  the  proportion  of  tho  radius  of  the  circum- 
ference of  the  wheel  to  that  of  the  axle.  That  is  to  say.  the  power, 
p,  is  to  the  resistance,  R,  as  the  radius,  b,  of  the  axle,  is  to  the 
radius,  a,  of  the  wheel,  or  the  length  of  the  winch  handh — in  the 
simpler  form  of  this  machine,  consisting  of  an  axle  and  a  winch 
handle.  The  same  rules  and  formulae  obviously  apply  to  this,  as 
to  the  first  described  form  of  lever. 

Thus,  multiply  the  resistance  by  the  radius  of  the  axle,  and 
divide  by  that  of  lie-  handle,  and  die  quotient  will  be  the  power. 

In  windlasses  and  cranes,  consisting  of  a  system  of  wheel-work, 
the  power  is  applied  to  a  handle  fixed  on  the  spindle  of  a  pinion, 
which  transmits  the  power  to  a  spur-wheel,  fixed  in  the  spindle  ot 
the  barrel,  about  which  the  cord,  or  rope,  carrying  the  load  to  bo 
raised,  is  wound. 

Where  there  are  several  pairs  of  such  wheels,  it  is  necessary  to 
include  in  the  calculations  the  ratios  of  the  pinions  to  the  spur- 

wheela 


TilK    VU\< 


•porlioeal  formula  will,  iu  thin  caae,  be  the  «ain. 

P:l::tx  V  <  y  ■.  a  *  • 

■ 

i    1/ 

.mrf  i/fruir  M- 
/>y  .'■"■  prrduct  of  Ote  radius  <f  the  handle  into  the  ru./ 

i       '  paoriatf  rill  oe  /Ac  potter,  ttkick,  rken  applied  to  rte 

li      W  '   -    ;■ 

trrd,  and  by  f  ■  .  and  the  quotient  will 

III.     1/      i  I  barrel,  and  Jiiulr  the 

.   :nd  the  quutirnl 

—When  ■  b 

plane,  i--  .  r,  and 

.-  none  of  the  weight  of  t!"  ..»,  but  manly 

■ 

mi  up  im  inettned  plane,  Ihi 
hi  proportionate  to  the  Inclination  of  ma 

'.  that 

f  ihr  flam  trill 

- 
— 

/  ON   the 
II     7 
III.   7 

i  of  the 

ombinod  wttfa  a 

■•  nda  upon  tlm 

Unll  ply  the 

the  i  nd  of  the 

arm  <r 

1  by  the 
nda  <>f 

- 


.'   »|a.  <■  [ rl 

■ 

— Tln-rv  art-  two  kim  tlie  one 

trawnjnj;  cclitrra. 

ng  ilio 

A  mii.  I   at  the 

eord,  ii  will  be  the  axis 

i  tlir  arrange- 

paaaod   through   l>y   I  the   latter  joae 

.  illey  will  onlj 
iror,  in  x  ti.  will  be  eqnal  to  thai  of  the 
in  eqafltbriam. 
Though    tip  i   u  i 

tnechan 
it  affordi 

■  pa.!  downward!  than  npwai 
■  In  the  formal  • 
Whan  several  pulleys  or  viiitja 

ndtahje  frame,  it  la  oallod  ■  blodt     Where  two  •  •r  mon 
■re  empJoyi  d,  it  i^  onlj  lb 
power,  and  thht 
or  pill!' 

Tin'  iin.liaiiiial  advantage  of  the  b  i 

■ 
tin-  ~un.  .  round  the  pul 

pi  txOng  t"  ii 
divided  bj  the  Dombi  i 

which  the  Hni  ■  pulley 

li\.  .1  in  the  w 

h  the  power,  i 
or  tnoti 

I  I 

I 
from  tin'  division  nt   • 

I 
over  which  tin   | 

understand,  that  when,  i ; 

"t  the  pow<  i 
■ 

tahed,  v 
rxtirlhj  I 

What? 

Iml    to 


BOOK   OF   INDUSTRIAL   DESIGN. 


circumstances  in  which  the  power  is  to  be  used.  Thus  we  can 
make  a  very  small  force,  as  that  of  a  man,  elevate  an  enormous 
weight,  but  with  a  speed  proportionately  slow. 

Finally,  The  mechanical  effect  developed  in  a  given  time  by  a  given 
force,  through  the  instrumentality  of  machinery,  must  always  equal  the 
useful  effect  obtained,  plus  the  amount  lost  in  overcoming  frictional 
and  other  resistances ;  and  the.  useful  effect  of  machinery  icill  he  the 
greater,  according  as  the  causes  of  these  resistances  are  diminished-. 

CENTRE    OF   GRAVITY. 

254.  All  bodies  are  equally  subjected  to  the  action  of  weight. 
Gravity,  or  weight,  is  the  action  of  that  universal  attraction  which 
draws  all  bodies  towards  each  other,  and  by  which,  in  the  case  of 
bodies  on  the  surface  of  the  earth,  these  are  drawn  towards  its 
centre.  The  power,  of  whatever  nature  it  may  be,  which  balances 
this  action,  is  equal  to  the  weight  of  the  body. 

The  curvature  of  the  surface  of  the  earth  being  quite  inap- 
preciable for  small  distances,  gravity  is  considered  as  acting  in 
parallel  lines,  and  its  direction  is  given  by  the  plumbline. 

The  centre  of  gravity  is  that  point  in  any  body  in  which  the 
action  of  its  entire  weight  may  be  said  to  be  concentrated.  If 
the  body  be  suspended  by  this  point  it  will  be  in  equilibria,  in 
whatever  position  it  is  put. 

The  position  of  the  centre  of  gravity  depends  upon  the  nature 
and  form  of  any  body ;  it  may  generally  be  found  in  the  follow- 
ing manner : — 

Suspend  the  body  by  a  thread  attached  to  any  point  whatever 
in  it ;  when  tho  body  is  motionless,  the  line  of  the  suspension 
thread  will  pass  directly  through  the  centre  of  gravity.  Suspend 
the  body  by  any  other  point,  and  the  centre  of  gravity  will  also 
be  in  the  continuation  of  the  line  of  the  thread,  so  that  the  actual 
centre  must  be  at  the  point  of  intersection  of  the  two  lines  thus 
obtained.  This  simple  expedient  reminds  us  of  the  application  of 
the  square  to  the  finding  of  the  centres  of  circles — the  unknown 
centre  on  the  endface  of  a  shaft,  for  example — where  the  inter- 
section of  any  two  lines,  drawn  along  the  blade  of  the  square, 
when  the  head  is  laid  against  the  periphery  of  the  shaft  iu  two 
different  positions,  gives  the  required  point  of  centre. 

The  centre  of  gravity  of  regular  bodies,  as  spheres,  cylinders, 
prisms,  is  in  the  centre  of  their  configuration. 

The  centre  of  gravity  of  an  isosceles  triangle  is  one  third  up 
the  centre  line  which  bisects  the  base. 

The  centre  of  gravity  of  a  pyramid,  with  a  triangular  or  poly- 
gonal base,  is  one  fourth  up  the  line  which  joins  the  summit  with 
the  centre  of  gravity  of  the  base.     It  is  the  same  with  a  cone. 

The  centre  of  gravity  of  a  hemisphere  is  situated  three-eighths 
up  the  radius  at  right  angles  to  the  base. 

The  centre  of  gravity  of  an  ellipse  is  in  the  point  of  intersection 
of  the  axes. 

When  a  body  is  placed  in  a  vertical  or  inclined  position  on  a 
plane,  it  is  necessary,  in  order  that  it  may  rest  upon  it  in  that  po- 
sition without  falling,  that  the  vertical  line  passing  through  tho 
centre  of  gravity  shall  fall  within  the  external  outline  of  the  side 
in  contact  with  the  plane.  This  limit,  however,  allows  of  consi- 
derable deviation  from  the.  vertical  in  the  general  contour  of  bodies, 
as  is  instanced  in  the  case  of  [canine  or  inclined  edifices.     The 


stability  of  bodies  increases  as  the  extent  of  their  bases  is  greater 

in  comparison  with  their  height,  and  also,  as  the  vertical  line, 
passing  through  the  centre  of  gravity,  meets  the  plane  on  which 
the  body  rests  nearer  to  the  centre  of  the  base.  A  body  is  said 
to  be  more  stable  when  it  requires  a  greater  force  to  overturn  it. 
A  cone  is  more  stable  than  a  cylinder  of  tho  same  height  and  base. 
The  stability  of  walls  depends  greatly  on  the  kind  of  foundations 
given  to  them,  and  on  the  proportionate  extension  of  their  bases. 

ON   ESTIMATING   THE   POWER    OF   PRIME    MOVERS. 

255.  As  we  shall  see  further  on,  the  power  of  prime  movers 
may  be  calculated  from  the  dimensions  of  the  various  parts  of  tho 
engine.  Still,  the  many  different  modes  of  construction  tend  to 
modify  considerably  the  actual  useful  effect,  and  engineers  have 
endeavoured  to  construct  an  apparatus,  by  means  of  which  the 
actual  power,  or  useful  effect  of  engines,  may  be  measured  with 
exactitude. 

Prony's  brake,  which  is  the  instrument  most  generally  used  for 
this  purpose,  acts  on  the  principle  of  the  lever,  and  consists  of  a 
cast-iron  pulley  in  two  halves,  united  by  screws.  This  is  fixed  on 
the  main  shaft  of  the  prime  mover,  the  force  of  which  it  is  wished 
to  measure.  It  is  embraced  by  two  jaws,  which  may  be  tightened 
down  upon  the  pulley  by  screws.  To  the  lower  jaw  is  attached 
a  long  lever,  from  the  end  of  which  is  suspended  a  scale  fi.r 
weights.  If  it  is  known  what  power  the  engine  was  designed  to 
possess,  it  is  simply  necessary  to  put  into  tho  scale  the  weight 
corresponding  to  this  power,  that  is,  the  weight  which,  by  tho 
action  of  the  lever,  will  give  a  pressure  equal  to  the  supposed 
power  of  the  machine. 

Having  fixed  the  apparatus  on  the  engine,  and  provided  means 
of  efficiently  lubricating  the  frictional  surface  of  the  pulley  with 
soap  and  water,  and  having  balanced  the  apparatus  in  such  a 
manner  that  it  will  not  be  necessary  to  take  into  tho  calci 
anything  but.  the  weight  placed  in  the  scale,  the  steam  may  be 
gradually  let  on.-  Tho  engine  will  perhaps  shortly  acquire  a 
greater  velocity  than  that  for  which  it  was  designed  :  it'  tlii-  is  the 
case,  the  jaws  are  gradually  screwed  closer  and  closer  upon  the 
pulley.  As  the  friction  thereby  increases,  the  velocity  will  dimi- 
nish, and  full  steam  may  be  let  on.  After  a  short  time,  and  when 
the  friction  is  so  great  that  the  lever  is  raised  slight]] 
the  horizontal  line,  and  the  engine  is  going  at  its  proper  velocity, 
and  the  pressure  of  tho  steam  at  its  correct  point,  so  that  tho 
power  of  the  engine  balances  the  load  on  the  lever,  it  may  fie  con- 
cluded that  the  engine  develops  the  power  for  which  it  was  in- 
tended. If  the  lever  rises  considerably,  it  will  !«•  necessary  to 
increase  the  weight  in  the  scale,  so  as  to  obtain  the  actual  maxi- 
mum power  of  the  engine ;  and,  on  the  contrary,  if  the  engh 
not  appear  to  have  the  desired  power,  the  weight  must  be  reduced, 
by  which  means  its  actual  p.>wcr  will  be  ascertainable. 

CALCULATION   FOR    THE    BRAKE. 

256.  The  weight  which  will  balance  the  force  of  a  machine  may 
1„-  calculated  when  the  length  of  the  lever  arm  is  known,  or,  m..ro 
correctly,  the  radius  from  the  centre  of  the  shaft  to  tin-  point  of 
suspension  of  the  weight,  and  the  nominal  horse-power,  by  the 
following  rule  : — 


TIIK    1 


. >  At  nominal  lonr-pomr  by  33.000,  «nJ  Win*  the  pro. 
duel  ty  At  cimmfrrmet  drteribtd  by  Ae  end  of  At  brer,  and  by 
At  number  <i  reiviutwni  per  ana**,  <m<i  Ike  fuofvaf  riU  bt  At 

for  . -uun|i!v,  the  main  ahaft  of  a  atom-engine  of 
r,   which   run*  it  the  rate  of  30  revolution*,  per 
minute,  tho  miiiu  of  the  brake  U-it 


! !  'iave  w  = 


■  =  311 


the  bra-  lUaotd   by  being  au-j-rmh-d  ..n  il» 

centre  of  gravity. 


The  actual    |  I  an  engine,  n-. 

r.ile : — 
!y  Ac  cireum/rrrnct  described  by  At  lexer,  by  At  number 
•  /  mvlutiuni  <f  At   tkafi  per  minute   aiJ  by  At  weight  ta  At 
teak,  and  dindt  At  prudmct   by  3X000  and  At  amUuml  trill  to 
At  actual /uret  <f  At  engine  in  bona  potter. 

■   tho  main  ahaft  of  a  atram- 
'  tat   the  ratiiua  of  the 
I  4  lba>, 
« kit  i»  tin   maximum  : 

114 


F  = 


I'll  P. 


TABLE    OF    I'" 


V.lunly. 

l|r,.ht 

1 

1 

ii.  atl 

Urkw. 

IwfcM. 

lack**. 

l-.s.. 

l.rW 

lack**. 

■artm. 

lartiM. 

Ik>.« 

6-8 

171 

1-473 

•8 

5-9 

177 

•4 

0-0 

1-4 

•J 

61 

•-. 

6  2 

19-0 

6-S 

19-5 

1-938 

•8 

64 

t 

85 

-215 

66 

11 

8-7 

6-8 

18 

6-9 

1  I 

15 

■oll5 

7  1 

18-5 

. 

61  5 

iTt 

21*86 

17 

7-8 

7   1 

63-0 

1-9 

8-316 

63'5 

s-o 

Jl 

i:.  in 

34-6V5 

86116 

S-8     * 

7-9 

- 

•328     . 

3-V96 

16  ■.■•■« 

-0319 

86 

8-3 

88 

• 

2-9 

8-0 

8« 

81 

•886 

81  5 

8-3 

■896 

8'8- 

89 

81 

88 -0 

85 

1  1 

885 

8< 

9-3 

8-7 

■0697 

9-8 

111 

84-5 

8-8 

8-9 

96 

86-6 

VI  S 

9< 

86-0 

41 

9'8 

4  8 

9-9 

6«-6 

11" 

4  7 

1174 

4Hi 

•999 

58 

-:. :.:..-. 

7H> 

S5-6V6 

55 

9C46 

99-6 

6"  466 

M 

1598 

16D 

*60?75 

BOOK  OF  INDUSTRIAL  DESIGN. 


THE    FALL   OF   BODIES. 

258.  Whon  bodies  fall  freely  of  their  own  weight,  the  velocities 
which  they  acquire  are  proportionate  to  the  time  during  which 
they  have  fallen,  whilst  the  spaces  passed  through  are  as  the 
squares  of  the  times. 

It  has  been  ascertained  by  experiment  that  a  body  falling-  freely 
from  a  state  of  rest,  passes  through  a  distance  of  16  feet  and  a 
small  fraction,  in  the  first  second  of  time.  At  the  end  of  this 
tune  it  has  a  velocity  equal  to  twice  this  distance  per  second. 

From  this  it  follows  that  if  the  tunes  of  observation  are — 


3" 


4" 
28  ft. 


"...  256" 

"...  112" 

2,  3,    4 

2,  3,    4 
4,  9,  16 

3,  5,    7 


The  corresponding  velocities  will  be         32  ft....  64  ft....  96  ft.. 
The  spaces  passed  through  from  the  )  .  „  „      fi .  ,,      .       ,, 

commencement,  ( 

The  spaces  passed  through  during  each  f  ,  fi  «     48  »       on  « 
second,  j 

That,  is  to  say,  that  the  times  are  as  the  numbers,    1,    5 
*The  velocities  also  as,  1,    S 

The  spaces  passed  through  as  the  squares,  1, 

Aud  the  space  for  each  interval  as  the  odd  numbers,  1, 

These  principles  apply  equally  to  all  bodies,  whatever  may  be 
their  specific  gravity,  for  gravity  acts  equally  on  all  bodies ;  the 
effect,  however,  being  modified  by  the  resistance  of  the  media 
through  which  the  bodies  pass,  which  is  greater  in  proportion,  as 
the  specific  gravity  is  less. 

259.  The  velocity  which  a  body  will  acquire  in  a  given  time 
when  falling  freely,  will  be  found  by  multiplying  the  time  ex- 
piessed  in  seconds  by  32  feet. 

Example. — Let  it  be  required  to  ascertain  the  velocity  acquired 
by  a  body  falling  during  12  seconds. 

V  =  12  x  32  =  384  feet  per  second. 

When  a  body  falls  from  a  given  height,  H,  the  ultimate  velo- 
city, or  that  acquired  by  the  time  the  base  is  reached,  will  be  given 
by  the  formula  (g  being  the  velocity  gravity  causes  a  body  to 
acquire  in  the  first  second) 


V  =  Vigil,  or  V  =  V64x  H, 
which  leads  to  the  following  rule : — Multiply  the  given  height  in 
feet  by  64,  and  extract  the  square  root,  which  will  be  the  velocity 
in  feet  per  second  by  the  time  the  body  shall  have  fallen  through 
the  height,  H,  not  taking  resistance  into  consideration.    * 

Example. — What  will  be  the  ultimate  velocity  of  a  body  falling 
a  distance  of  215  feet  t 


H  =  —  = 


V  =  V64  x  215  =  117-3  feet  per  second. 
From  the  above  formula, 

\  =  V2g-R, 
we  obtain  VJ  =  2  g  H,  then 

64' 

whence  we  have  this  rule : — Divide  the  square  of  the  velocity  in 
feet  per  second  by  64,  and  the  quotient  will  express  the  height 
through  which  a  body  must  fall  unimpeded,  from  a  state  of  rest,  in 
order  to  obtain  that  velocity. 

Example. — A  body  has  acquired  a  velocity  of  1173  feet  per 
second,  through  what  height  must  it  have  fallen  ? 

H=  =^-  =  215  feet,  the  height  of  the  fall. 
64 

To  obviate  the  necessity  of  calculating  the  corresponding  heights 

and   velocities,   we   give   a  very   extensive   table,  calculated   for 

tenths  of  inches      The  numbers,  however,  being  equally  correct 


as  representing  feet  or  yards,  thoso  of  both  columns  being  of  tlio 
siune  denomination. 

MOMENTUM. 

260.  Tho  force  with  which  a  body  in  motion  strikes  upon 
one  in  a  state  of  rest,  is  equal  to  tho  product  of  tho  mass  of 
the  moving  body  multiplied  into  the  velocity;  this  product  is 
termed  its  momentum.  If  a  body  with  a  mass,  m,  is  animated 
with  a  velocity,  v,  its  momentum  is  equal  to  m  v.  The  term,  m, 
however,  may  be  taken  as  signifying  the  mechanical  effect  of  a 
weight  falling  during  a  second  of  time,  or  through  32  feet,  there- 

20 

fore,  m  =  — ,  that  is,  tho  weight  in  pounds  divided  by  32  feet, 

w  x  v 

whence,  m  v  =  • 

What  distinguishes  the  simple  momentum  or  force  of  impact  of 
a  body  from  the  mechanical  effect  of  a  prime  mover  is,  that 
whilst  the  former  is  due  to  a  single  impulse,  we  have  in  the  latter 
to  consider  the  continuous  action  of  the  impelling  force. 

261.  When  a  motive  force  imparts  continuously  a  certain  velo- 
city to  a  body,  the  result  of  its  action  is  what  may  be  termed  I  is 
viva,  or  continuous  momentum;  it  is  numerically  the  product  of 
the  (moving)  mass  multiplied  into  the  square  of  the  velocity  im- 
parted to  it. 

Putting  M  to  represent  the  mass  of  a  body,  and  V  the  velocity 
impressed  upon  it, 


M  VJ  or 


WV 
g 


is  the  expression  of  the  ozs  viva  of  the  body.  This  force  is  doublo 
that  developed  by  gravity.  For,  in  fact,  when  a  body  of  the 
weight,  W,  falls  from  a  height,  II,  it  acquires  from  its  fall  an 
ultimate  velocity,  V,  which  we  have  already  shown  to  be  equal  to 

and  the  mechanical  effect,  W  H,  is  consequently  expressed   by 

WV 

*g  ' 

U  v 
now,  putting  for  P,  its  value,  Mir,  the  formula  becomes  — g—  • 

Thus,  the  mechanical  effect  developed  by  gravit]  is  equal  to 

half  the  vis  viva  imparted  to  a  body. 

CENTRAL    FORCES. 

262.  When  a  body  revolves  freely  about  an  axis,  it  is  said  to 
be  subjected  to  two  central  forces;  tin  *  one,  termed  "centripetal," 
tends  to  draw  the  body  to  the  axis;  the  other,  termed  "  centri- 
fugal," or  tangential,  and  due  to  the  tendency  of  bodies  in  motion 
to  proceed  in  straight  lines,  strives  to  carry  the  body  away  from 
the  centre.  These  forces  aro  equal,  and  act  transversely  to  each 
other. 

The  centrifugal  effort  exerted  by  a  body  in  rotative  motion,  and 

which   tends  to   separate   the  component  particles,  is  e\pn  - 

the  following  formula  : — 

W  V 

F . 

i'xR' 

in  which  W  represent.-  the  weigh!  of  the  body;   V,  the  velocity  in 


Tin:   i 


-  orcuad ;  and  U,  the  radius,  or  distanc*  at  the  centre  of 

: 

I  of  the  Weir 
radius,  It,  Hi. ..  rotate  with  a  velocity,  V  =   . 


ball  oa 
Uk  r»  . 


F  = 


•J3  X  40  X  40 
Si  x  a 


=  230  lbs.  raise! 


rilUTF.K    VII. 


ELEMENTARY    PEINCIPLES    OF  SHADOWS. 


trical  drawing,  that  Uu 
■ 

from  tin-  upper  left  hand  ooi 

:!iai  tli«-  horizontal  at 
cubic  diagonal  make  angles  of  45'  with  tin 
I 
The  .  this  assumption  of  the  <iir.  eiion  of  the  my* 

it  has  the  merit  of  n' 

is  parts  of  an  object,  even  with 
or  view. 

rtnined,  on  considering  an  ob- 

■"■  tiii  ■  cyiindri- 
of  which  will  In'  tin'  Ulaminod 
The  part  ni.-t  by  the**  rmyi  of 
Iflumined,  whOal  the  )>orti..: 
entire!)  (hi*  latter  |iart 

I  roptr  «f  the  object — I 

•  ray*  surrounding  the 
ted  by  I 

will   hi'   unillu- 

■  "f  the  interception  of  -•< f  the  r.;\-  by  the 

Hon  will  be  limited  by, 

ned  tlie 

■    i  any  virfai-e. 
■    'In-  illumine.)    from    the  litiilliimiued 
|  .  or  (lie 

ihadow.    Tlii"  ii  modified  by  the  form  of  the  red. 
•rail  aa  by  thai  of  the  object  which 
l  'a  Usee  when  • 

are   plain.;  and    by    rum  -  wh.n   either  or    b"lh   tire   cylindrical, 

• 

■  ■•  rniitiati.in    of   tli Uloi  •.    ,,f 

•  proper,  and  i  ■  Boding 

tlii-  |H.n  '  •  a  straight  lite 

with  a   ;  I 

■  by  tli" 
'-,  and  it  i.  neeoaaarj 


•  \  plain  the  aunt 
which  n  a  due  regard 

■ 

i,  ainl  bounded 

ally  cylindrical ;  ainl  we  shall  proa 

complex  form*.     The  objecta  which 

'.lv  met 
with  in  machinery  and  architecture;  they  will,  n 
afford  quite  sufficient  illustration  in  i 

XXVI. 

the  horizontal  and  ra> 
tieal  projection*  of  a  cube,!!  b  required  to  determine  the  fonn 

In  th' 

wliieli  are  in  tin   light  are  tie  by  a  D  ainl  A  C,  in   the 

horizontal  projection,  anJ  p  ly  in  a'  t'  u 

The  op;  1  o,  are 

in  the  n  pri -i  ntations,  the  - 
can  only  l»-  ahown  l>y  a  thick  shadow  line,  produced  by  China  ink 

in  line  d/nwii     •  -r..k,    of  the   l.ru-li  in  w.iler- 

Coliiiir  ilr- 

i       •    lines,  which  distinguish  the  illumii 
from  tie 

ation  of  Ugbl  and  shade.    It  now  •  find  Um 

shallow  cast  by  the  cube  on  the  plane,  i.  t. 
When  the  obji  cl  r.  ita  on  thi 

•  from  the  rerl 
|i  equal  '  by  it  will  !»■  in  the 

■   I   plane;  and  to  '!•  tenuine  it-  outline  bi 

.  u  K  in/,  parallel  to  i 

liliil  the  l-'int.",  c  h,  ,1,  in  which  tie  *••  line  BMaj  tie 

To  •fled  thla,  through  the  points,  o*,  and  a',  flg,  i  <;.  the  pro. 

.1   the  tWO  lir-t.  H  D,  'haw   t1  n.l  a'  b',  |*rsl- 

lel   to    it',  ami   meeting  the  baa*  line,  i.  T,  in  e*  and   ■'.      I 

through  th***  points,  w*  'haw  p.  rpeadfcnlar*  to  the  l 

...  «in  ,-nt  thi  i  lour  "f 

.  liinite.l  by  tl" 
/• ./,  ami  i/  o. 


BOOK   OF    INDUSTRIAL   DESIGN. 


The  faro,  e'  e',  being  that  on  which  the  cube  rests,  has  no  pro- 
minence, and  caunot  therefore  cast  any  shadow.  It  follows,  then, 
that  the  shadow,  as  above  determined,  is  all  that  is  apparent.  It 
is  generally  represented  by  a  flat,  uniform  shade,  laid  on  with  the 
brush,  and  produced  by  a  greyish  wash  of  China  ink. 

269.  It  will  be  observed  that  the  lines,  d  b  and  b  c,  are  parallel 
to  the  straight  lines,  D  B  and  B  c.  This  is  because  these  are 
themselves  parallel  to  the  horizontal  plane ;  for  when  a  line  is 
parallel  to  a  plane  (82),  its  projection  on  this  plane  is  a  line  paral- 
lel to  itself;  and  hence  we  have  this  first  consequence,  that — 

]\~hen  a  straight  tine  is  parallel  to  the  plane  of  projection,  it  casts 
a  shadow  on  llie  plane,  in  the  form  of  an  equal  and  parallel  straight 
line. 

270.  It  will  also  be  observed,  that  the  straight  lines,  d  d,  b  b,  c  c, 
which  are  the  shadows  east  by  the  verticals,  projected  in  D,  B,  and 
c,  are  inclined  at  an  angle  of  45°  to  the  base  lino ;  whence  we 
derive  the  second  consequence,  that — 

When  a  straight  line  is  perpendicular  to  the  plane  of  projection, 
it  casts  a  shadow  on  the  plane  in  the  form  of  a  straight  line,  parallel 
to  the  raijs  of  light,  and  consequently  inclined  at  an  angle  of  45"  to 
the  base  line. 

271.  These  observations  suggest  a  means  of  considerably  simpli- 
fying the  operations.  Thus,  in  place  of  searching  separately  for 
each  of  the  points,  e,  b,  d,  where  the  rays  of  light  pierce  the  hori- 
zontal plane,  it  is  sufficient  to  determine  one  of  these  points,  such 
as  6,  for  example,  and  through  it  to  draw  the  straight  lines,  b  d,  b  c, 
parallel  and  equal  to  the  sides,  D  B  and  B  c,  of  the  cube  and 
intersecting  lines,  inclined  at  an  angle  of  45°  drawn  from  the 
points,  D  c. 

In  the  actual  case  before  us,  we  may  even  entirely  dispense  with 
the  vertical  projection,  fig.  1",  since  it  would  have  been  sufficient 
to  prolong  the  diagonal,  a  b,  to  b,  making  b  B  equal  to  n  a.  or  to 
make  the  inclined  lines,  d  d,  or  b  b,  equal  to  the  diagonal,  A  B ; 
because  the  vertical  projection,  c'  c',  and  horizontal  projection,  c  c, 
of  the  same  ray  of  light,  are  always  of  the  same  length,  which  fol- 
lows from  our  having  taken  the  diagonal  of  the  cube  for  the  direc- 
tion of  this  ray,  the  two  projections,  a  b  and  a'  b',  of  this  diagonal 
being  obviously  equal.  Whence  follows  the  third  consequence, 
that — 

//',  through  any  point  of  which  the  two  projections  are  given,  we 
draw  a  straight  line,  representing  the  ray  of  light,  and  if  we  ascer- 
tain the  point  in  which  this  ray  meets  either  plane,  the  length  <f  the 
ray  in  the  other  plane  of  projection  will  be  the  same. 

2T2.  Finally,  it  is  to  be  observed  that  the  distance,  b  d,  taken 
on  the  prolongation  of  the  vertical  line,  c  b,  is  equal  to  the  entire 
height,  c'  b',  namely,  that  of  the  cube  ;  and  consequently,  in  place 
of  employing  the  diagonal  to  obtain  the  various  points,  d,  b,  c,  we 
may  make  the  distance,  B  d,  equal  to  the  height  of  the  cube,  and 
draw,  through  d,  a  straight  line,  d  b,  parallel  and  equal  to  db, 
and  through  b  a  second,  b  c,  parallel  and  equal  to  b  c,  and  then 
join  d  D,  c  c. 

Thus  the  shadow  cast  on  a  plane  by  a'  point,  is  at  a  distance 
from  the  projection  of  the  point,  equal  to  the  distance  of  the  point 
itself  from  the  plane. 

273.  Figs.  2  and  2"  represent  a  prism  of  hexagonal  base,  sup- 
posed to  be  elevated  above  the  base  line,  but  at  the  same  time  at 


such  a  distance  from  the  \crtical  plane,  that  all  tin-  shadow  i;tst 
will  be  in  the  horizontal  plane. 

It  will  be    seen    that    the  vertical    faces,   a  b,   b  C,  and  A  F,  aro 

illumined,  whilst  the  opposite  ones,  e  d,  d  c,  and  Br,  are  in  the 
shade. 

Of  these  latter  faces,  c  D  is  the  only  one  visiblo  in  the  vertical 
projection,  fig.  2*,  and  represented  by  the  rectangles  c'  d'  H  g, 
which  should  be  shaded  to  a  deeper  tint  than  the  CflBl  shadows, 
to  distinguish  it. 

274.  The  operation  by  which  we  determine  the  shadow  cast 
upon  the  horizontal  plane,  is  evidently  the  same  as  in  the  preced- 
ing case;  still,  since  the  lower  base,  j  h,  does  not  rest  upon  the 
horizontal  plane,  it  will  not  be  sufficient  merely  to  draw  the  rays 
of  light  through  the  points,  c,  d,  E,  f,  of  the  upper  side ;  it  is,  in 
addition,  necessary  to  draw  corresponding  rays  through  the  points, 
J,  I,  G,  H,  of  the  base. 

It  is  to  be  observed,  as  in  the  preceding  case,  that  as  these  two 
faces  are  parallel  to  the  horizontal  plane,  the  Bhadow  cast  by  each 
upon  this  plane  will  be  a  figure  equal  and  parallel  to  itself;  so  that, 
in  place  of  seeking  all  the  points  of  the  shadow,  it  would  ha\e 
been  quite  sufficient  to  obtain  one  of  these  points,  as  d.  for 
example,  of  the  upper  side,  and  k,  of  the  lower  side,  and  then, 
starting  from  them,  to  draw  a  couple  of  hexagons,  parallel  and 
equal  to  a  n  c  D  E  F. 

It  will  also  be  understood,  that  as  it  is  only  the  outside  lines, 
those  of  the  separation  of  the  light  and  shade,  which  make  up  the 
contour  of  the  shadow,  it  is  not  necessary  to  determine  the  points 
which  fall  within  this  contour,  and  correspond  to  those  points 
in  the  object  itself  which  do  not  lie  in  the  lines  of  separation  of 
the  illuminated  and  shaded  parts. 

275.  Thus  it  is  unnecessary  to  find  the  points,  a,  b.  e,  h  ;  and 
generally,  in  making  drawings,  we  do  not  seek  tin-  shadows  cast 
by  points  fully  illuminated,  or  within  the  borders  of  the  shaded 
portion;  and  the  contour  of  the  shadow  is  derived  simply  from 
points  lying  in  the  line  of  separation  of  the  light  and  shade  on  the 
object. 

276.  From  what  we  have  already  explained,  it  will  In-  gi 

that  the  projection  in  one  plane  of  the  Bhadow,  cast  by  a  point,  •■■■■  i 
be  obtained  by  drawing  the  diagonal  of  the  Bquare,  a  Bide  of  which 
is  equal  to  the  distance  of  the  point  from  the  plane,  as  shown  in 
the  other  projection. 

For  example,  the  shadow,  k,  on  the  horizontal  plane  of  the 
print    the  two  pi-j.-_i!  ms  ot  win-  h  air  i   and  I.  li.  >.  ..  an!  .:    in:' 

be  got  by  forming  the  Bquare,  i  Ik,  a  side  of  which,  r  /.  i 
to  the  distance,  i  /',  of  the  point  from  tie-  horizontal  plane. 

In  the  same  way,  we  have  the  points,  g,  i,f,  corresponding  to 
g.  t,  r.  whi.h  are  the  same  height  as  the  first  above  the  plane. 

For  the  points,  c,d,  e,f,  which  correspond  to  the  upp 
a'd',  of  the    prism,  we    draw  the   diagonal,  1/  </',  of   l!,. 

having  for  a  side   the   height,  o'tn,  of  the  poist,  d',  above  the 

horizontal  plane,  and  set  out  this  diagonal  from  C  to  c,  D  to  a, 
E  to  e,  &c 


277.  When   several   straight   lines   converge   to  a   point,  the 
shadows  they  cast  on  either  plane  of  projection  must  necessarily 


TIIK.    PRACTICAL   I»It  M'lillT- 


■bo,  cuniotga  to  •  p"ir.t.  Thus,  in  the  p>  raroid,  figa.  3  and  3*. 
Ib»  aprx  of  whirs  U  projected  in  the  pointa,  «  and  »'.  Ihc  edgea  of 
all  the  aide*  brine  directed  to  thia  point,  caat  shadow,  on  tho 
horizontal  plane,  bounded  by  line*  corner.  '.  a,  the 

ahadow  caat  by  the  »|»v  on  the  name  plane.  In  OfdaT,  then,  to 
find  the  ahadow  east  by  a  \-\  n 

•  .  draw  the  ray  of  li^'ht  through  the  apex, 

■     ' 
draw  linea  to  thin  point    fr-  tn  all  1 1  •   la-    of  the 

pyramid,  if  thia  mil  U|>on  the  plat;.       I 

b  raiaed  above  the  plane,  it  will  !-■  neceHw.  ladowa 

caat  by  the  various  angles  of  tin-  base,  and  thin  draw  straight 
linea  from  tbeae  to  the  ahadow  of  tin-  apex. 

•    rVKAMID. 

of  a   pyramid   I 
with,  and  the  ■)  i.  it  is  neeeaaary  lo  Bod  tin  - 

ban,  ami  by  t 
truncation.     Tims  tli. 

-  on  the  borizotttal   plana,  in  the  \- 
whteh  are  obtained  by  drawing  nroogh  each  point,  in  tin- 
I 

-  './..IT.  •*,  which  are  wjna: 

In  Ibc  borizonb  -  aa  t<>  meet  the  com 

drawn  through  tin-  pointa,  r.,  f,  q,  ii.  Then,  it'  «r  dm  lines 
from  t!  I  in  tho 

la]  plan.-,  wc  hhall  ohtain  tl.-  •    by  null  of  the 

lateral  edges  of  the  pyramid. 

W  aamc  reason  that  these  edj.'es  are  diver*  ly  inclined  to 

-t  by  tin-in  on  tins  plane  have 

r.  nt  inclinations  to  the  base  lino;  but the  adgoa  of  the 

paraDal  to  tl.  - 
:  parallel  to  tl  - 
been  the  rase  bail  i'  i   to  the 

l       •  rident  that,  in  tbe  position  in  which  the  pyramid  in 

-    A  E  H  D 

and  a  r.  r  n,  an-  in  the  li^'lit,  whilst  tin -ir  oppoaites,  D  11 
c  o  r  b,  are  in  the  abode.     This  bat,  wbJafa  ia  tlie  only  oni 
in  fig.  3*,  ia  there  dbtinguished  by  a  nodi  rate  abada  of  colour. 

■her. 
!i  n  circular  bna  being  a  regular  solid,  all 
that  is  I  ■   running  tbe  Bam  of  separation  of  lieffit  and 

shade,  in,  nli.-n  tin-  cylinder  is  \ertical,  to  draw  a  couple  •  ■' 
tangential   to  it,  ami  |mrallel  to  tin-  a,  4  and 

4*.    n  a  the  borlsontal  plane, 

in  the  linen,  ao,  it,  tangent*  to  tbe  cfaele,  and  inclined  at  the 

By  with   tbe  i-in 

iration  of  lighl  and  shade,  which  are 

ally  in  a'  c  and  a*  D  i  b  appa- 

V.  •   hajaa  tlmi  thl    . 

a  r.  a,  o  in  the  light,  at  .  a  r  n,  in  tbe 

aluule.     A  very  small   portion   of  tbii  lout  r.  anil  is 

• 

hailo«,  it  i«  t,,  l„.  remarked, 
that  for  the  very  reason  Oiat  Be  line*  of  separation  of  light  and 


aluule  are  vertical,  the  ahad- 

plane  w  I  Baa,  e  a  and  J  b,  with  an  in. 

. 
l-arallel  to  the  horizontal  pla: 
-  Ives ;  and  all  that  ii 
caat  b\  '  —,  x  and  &,  and  w ith  tbe  pointa,  a,  a, 

-    with  a  radii;-  L     The 

■iln,  c  a,  J  b. 

.    Villi    AloTHIft. 

ML  Hitherto  we  I. .  -i  by  an 

I 
r,  that  one  bod) 

a  of  the  1h«1i  at  one  part  of  it  caata 

■    iln-r. 

•:  of  a  short   ,- 

'•'■ 

linil  the  line  of  eeparation  i  abada  npoo  tb 

cylinder* ;  and  lor  tl.  • 
tbe]  projeedon, 

ofitanx          '  Jit  also 

I 
ilniw  tb 

a'  and  B ,  anil  i  '.  r*  and 

(/',  to  Bg.  I  and  D  tl.  which   separate  tho 

tight  iVom  tie  -                                            I                 drawing 

draws 

I.  n,  upon  tlio 
cylinder,  a,  is  limited  to  that  due  to  the  |>ortion.  <f  r'  ir\  of  tbe 
cin-uiui.  I  nt  poiaia  in  the  on:  low  are 

determined,  by  first   taking  any   pot  .  upon  the  arc, 

i/'  •    li',  and  drawing  throogh  each  of  them 
parallel  rays  of  light,  and  lie 
der,   a',  in   tbe    point-,   c\  r\   /",  a*.      Ha\i 
mention. si  |„,inis  on  ti 

•    parallel    to    the    first,    and 
-  of  light,  and  square  on  r  lb 
wbi.-h   will  | 

-  the  onijiii-  of  the  abadow*apoo  tb 

Aa  jieen   in   a  fonm  r   exainple,   bjataad  nrot   tbe 

|  .  »e  can  obtain  bV  log  the 

■lidino  rays  I 

MIAMiW  I  *ST   BY   A  CVLI5nr.K   fro*   a   ruts*. 
383.  Figa.  7  1  anaofa  prism, 

a,  of  an  nulagnnal  ban  '.  »• 

\  draw  tbe   ra.i 

a  of  liirii'..  tiienby  obtaining  tbe  point  of  contact,  if,  and, 
tlio  line  of  «e|»aratioii.  n  J,,,f  hght   and  - 

tbe  oyhndrical  1 1 

•    the  prisra.  being  in  tbe  dir.  ■ 
the  ray  of  light,  ami,  consequently,  bclined  at  an  angle  of  I 


BOOK  OF   INDUSTRIAL   DESIGN. 


the  vertical  plane,  is  considered  to  be  completely  in  tho  shade. 
The  edge  line,  a  b,  fig.  7,  is  therefore  the  lino  of  separation  of 
light  and  shade  on  the  prism-shaped  portion  of  the  object,  and 
the  surface,  a  bid,  is  consequently  tinted.  The  shadow  cast  upon 
the  prism  by  the  overhanging  head,  e,  reduces  itself  to  that  due  to 
the  portion,  c'  f'  h',  merely,  of  the  circumference  of  the  latter,  and 
it  falls  upon  the  two  faces,  c'  f  and/"  ft',  of  the  latter. 

The  lines  indicated  on  the  diagram,  with  their  corresponding 
letters,  when  compared  with  those  of  the  preceding  example,  will 
show  that  the  operations  are  precisely  the  same  in  both  cases,  and, 
in  the  latter,  the  curves,  c  ef  and  fg  h,  are  the  resulting  outlines 
of  the  shadow.  In  general,  it  is  unnecessary  to  obtain  more  than 
the  extreme  points  of  the  curve,  and  another  near  the  middle. 
•  Through  the  three  points  thus  obtained,  ares  of  circles  can  then  be 
drawn.     The  curves  are,  however,  in  reality  elliptical. 

SHADOW  CAST  BY  ONE  PRISM  UPON  ANOTHER. 

284.  Figs.  8  and  8"  represent  a  couple  of  vertical  projections,  at 
right  angles  to  each  other,  of  a  prism  of  an  octagonal  base,  sur- 
mounted by  a  similar  and  concentric,  but  larger  prism.  Although 
the  operations  called  for  in  this  case  are  precisely  the  same  as  in  the 
two  preceding,  still  it  is  an  exemplification  which  cannot  be  omitted; 
and  its  chief  use  is  to  show,  that 

The  shadow  cast  by  a  straight  line  upon  a  plane  surface  is  inva- 
riably a  straight  line ;  and,  consequently,  it  is  sufficient  to  determine 
its  extreme  points,  in  order  to  obtain  tlie  entire  shadow  in  any  one 
plane. 

Thus,  the  straight  line,  e'  c',  easts  a  shadow  upon  the  plane 
facet,  fc,  which  is  represented  by  the  straight  line,  ec. 

It  is  further  obvious,  that 

The  shadow  cast  upoti  a  plane  surface,  by  any  line  parallel  to  it, 
must  be  parallel  to  that  line. 

Thus,  the  straight  line,  e'  g',  of  the  larger  prism,  B,  being  paral- 
lel to  the  plane  facet,  f  g',  of  the  prism,  a,  casts  a  shadow  upon 
the  hitter,  which  is  represented  by  the  straight  linc,/g-,  parallel  to 
the  line,  F  G,  the  vertical  projection  of  the  edge,  f'  g'.  It  is  not, 
however,  the  same  with  the  portion,  ef,  because  the  coiTesponding 
portion,  e'  f',  of  the  edge  of  the  larger  prism,  is  not  parallel  to  the 
facet,/  e1. 

SHADOW   CAST   BY   A   PRISM   UPON   A   CYLINDER. 

285.  Figs.  9  and  9"  represent  vertical  projections,  at  right  angles 
to  each  other,  of  a  portion  of  an  iron  rod,  a,  surmounted  by  a  con- 
centric head,  B,  of  a  hexagonal  base.  The  main  object  of  tliis 
diagram  is  to  show,  that 

When  a  right  cylinder  is  parallel,  or  perpendicular,  to  a  plane  of 
projection,  any  straight  line,  which  is  perpendicular  to  the  axis  of  the 
cylinder,  and  parallel  to  the  plane  of  projection-,  casts  a  shadow  upon 
the  cylindrical  surface,  which  is  represented  by  a  curve,  similar  to 
the  cross  section  of  such  surface. 

If,  therefore,  the  cylinder  is  of  circular  base  or  cross  section,  as 
we  have  supposed  in  the  present  case,  the  shadow  cast  upon  it 
will  be  a  portion  of  a  circle,  of  the  same  radius  as  the  cylinder. 
Thus,  the  straight  line,  d'  f',  situated  in  a  plane,  at  right  angles  to 
tho  axis  of  the  cylinder,  a,  and  being,  at  the  same  time,  parallel  to 
the  vertical  plane,  casts  a  shadow  upon  the  cylinder,  which  is  re- 


presented by  the  portion,  c  c/,  of  a  circle,  the  centre,  «',  of  which  is 
obtained  by  drawing  through  the  point,  o,  a  line,  o  i,  representing 
tho  ray  of  light,  and  extending  to  the  prolongation  of  the  edge,  d' 
f'.  Tho  line,  o  I,  cuts  the  circumference  of  tho  cylinder  in  the 
point,  i',  which  is  squared  over  to  i,  upon  tho  other  projection,  h  i, 
fig.  9,  of  the  ray,  o  I.  The  lower  point,  c,  is  obtained  from  tin- 
upper  one,  t',  being  symmetrical  with  reference  to  the  axis  of  the 
cylinder.  Tho  ray,  H  t,  being  continued  to  the  axis,  cuts  it  in  the 
point,  o',  which  is,  consequently,  the  centre  of  tho  arc,  c  i ■  i,  the 
radius,  io'or  co',  of  which  is  equal  to  that,  o  i',  of  the  cylinder. 

286.  The  edge,  f'  h',  although  situated  in  a  plane  perpendicular 
to  the  axis  of  the  cylinder,  is  not  parallel  to  the  vertical  plane,  and 
does  not,  therefore,  cast  a  shadow  of  a  circular  outline  upon  tho 
cylinder,  but  one  of  an  elliptical  outline,  as  fg  h,  which  is  obtain- 
ed by  means  of  points,  tho  operations  being  fully  indicated  on  tho 
diagrams.  If  the  head,  b,  which  casts  a  shadow  upon  the  cylin- 
der, were  square,  instead  of  hexagonal,  as  is  often  the  case,  one 
of  tho  sides  of  the  square,  as  I  n',  fig.  9*,  being  perpendicular  to 
the  vertical  plane,  would  cast  a  shadow  on  the  cylinder,  having 
for  outline  the  straight  line,  H  i,  making  the  angle  of  45°  u  ith  the 
axis. 

Thus,  wlienever  a  straight  line  is  perpendicular  to  the  plane  if 
projection,  not  only  is  Us  shadow,  as  cast  upon  this  plane,  a  straight 
line,  inclined  at  the  angle  of  45°,  but  it  is  also  the  same  on  an  object 
projected  in  this  plane,  no  matter  of  whafform. 

Observation. — In  the  four  examples  last  discussed,  we  have  only 
represented  half  views  of  the  objects  in  the  auxiliary  vertical  pro- 
jections, figs.  6",  7,"  8",  and  9*,  this  being  quite  sullicienl  for  deter- 
mining the  shadow,  as  it  is  only  that  produced  bj  this  half  which  is 
seen.  It  is  obvious,  that  the  same  operations  will  answer  the  pur- 
pose, whether  the  axis  of  the  object  be  horizontal  or  vertical. 

SHADOW   CAST   BY   A   CYLINDER    IN   AN   OBLIQUE    POSITION. 

287.  In  figs.  5  and  5',  we  have  given  the  horizontal  and  vertical 
projections  of  a  right  cylinder,  having  its  axis  horizontal,  but 
inclined  to  the  vertical  plane.  As  in  this  oblique  projection  we 
cannot  obtain  the  points  of  contact  of  the  luminous  rays  with  tho 
base  in  a  direct  manner,  it  becomes  necessary  to  make  an  especia. 
diagram,  in  order  to  determine  the  lines  of  separation  of  light  and 
shade,  which  are  always  straight  lines,  parallel  to  the  axis  of  the 
cylinder. 

To  this  effect,  we  shall  make  use  of  a  general  construction,  sus- 
ceptible of  application  to  a  variety  of  such  cases.  This  construction 
consists  in  determining  the  projection  of  the  luminous  ray,  in  any 

given  plane,  perpendicular  to  either  of  the  geometrical  planes,  w  hence 

may  be  derived  its  form  and  aspect  in  either  of  the  latter  planes. 
It  follows,  that  if  we  have  any  curve  in  the  given  plane,  we  can 
easily  find  the  point  of  separation  of  the  light  and  shade  situated 
upon  this  curve,  by  drawing  a  couple  of  tangents  to  it,  parallel  to 
the  ray  of  light  projected  in  this  plane,  and  transferred  to  the  otlier 
plane  of  projection. 

Thus,  let  r  o  and  r'  o'  be  the  projections  of  the  luminous  ray . 
it  is  proposed  to  find  the  projection  of  this  ray  upon  the  plane,  a  b, 
of  the  base  of  the  cylinder.  To  obtain  this,  project  the  point,  R 
to  r,  by  means  of  a  perpendicular  to  a  b,  and  r  o  represents  tho 
horizontal  projection  of  the  ray  of  light  upon  the  plane,  a  b;  and 


' 


.-.Iby  •qu«riri. 
*-.-  lrn<\  tmi  /■•utal. 

•  Ittpeea, 

»',  .-'.   :.  ■  -.  ..  nl   ''  •    *•  r-  ..-.i!   |«  .yvtii.ru  (.f  the  .I'd'  .-I   ill.-  .  Win. I.  r. 
taking  three  Uageota  far:. 

- 

I  and/e, 

;  independently 
5",  in  the  Colli 
i-  at  a"  b\  haril 
• 
the  raj 

• 

>  of  the 

<i'  m  //*, 

paraJli-l  t.>  •>  r\  ami  tl  •  -  nt  the 

.nl.-.  ulii.h  are 
the  horizontal   |  ..iiculara 

drawn  from  tl 

en  thus 
be  difficult  t<>  find  tin 
i 
■ 

..  those 

- 

-•  parallel  to  the  line,  r*  o. 

I,  in  the  ho riAnnt.il  pro- 
1  with  the  extn 

I 
■ 
and  «  paria. 


PRINCIPLES  OP  SHADING. 

Purr   XXVII. 

-should 


difficult  •  .wily  Miniii.tn  ■ 

light  and  iJia.1- 

- 
II  an  illumined  surface  has  all  its  points  at  an  equal 

from  the  eye,  it  must  rceru*  a  clear  shade  of  uniform  inten- 
sity Aroughnut. 

-  ippoaed 
to  be  parallel  nii.l  perpendicular  to  tl  all  »ur- 

• 

■ 

'  I  -  illel  to  tarn  ether,  and 

illumin  manner,  that  which  is  nearer  to  the  eye  should 

■nsity. 
\  '.  inclined  to  the  plane  of  tfte  picture, 

.•lances  from  the  ry. 

■      ■  : 

portion  of  an  ob  ur;  thi* 

■ 
i  at  which  is  mitrr  directly  pre- 

- 
- 
still,  at  i 

- 

H 

m  inten- 
sity throm 

•  \  VIII.,  whi  h 

pon  i ho 

more  pi 

i. in-  in  ;  tj   with  the  tw 

I 

•  -  tint. 
.-!  upon  the  t  x  Will  . 

M 

\ 

li-rably 
•  ■  £*• 


BOOK  OF   INDUSTRIAL  DESIGN. 


297.  IV7ien  two  surfaces  in  the  shade  are  unequally  inclined, 
u-ith  reference  to  the  direction  of  the  rays  of  light,  the  shadow  cast 
tnj  any  object  should  be  deeper  upon  that  which  receives  it  more 
a  i  recti  y. 

Thus,  the  shadow,  a  dfe,  east  upon  the  faee,  f,  of  the  prism, 
fig.  1,  Plate  XXVI.,  should  be  slightly  stronger  than  that  cast 
upon  the  face,  g,  because  the  first  is  more  directly  presented  to 
the  light  than  the  second,  as  shown  by  the  lines,  /'  h'  and  /'  c', 
fig.  7". 

These  first  principles  are  exemplified  in  the  finished  figures  on 
Plate  XXVI.,  XXVII.,  and  subsequent  ones. 

As,  in  order  to  produce  the  gradations  of  shades,  it  is  important 
to  have  some  knowledge  of  actual  colouring  or  shading  by  means 
of  the  brush,  we  shall  proceed  to  give  a  few  short  explanations  of 
this  matter. 

Two  methods  of  producing  the  graduated  shades  are  in  use — 
one  consisting  in  laying  on  a  succession  of  flat  tints ;  the  other,  in 
softening  oft*  the  shade  by  the  manipulation  of  the  brush. 

We  have  already  said  two  or  three  words  about  the  laying  on  of 
flat  tints,  when  treating  of  representing  sections  by  distinguishing 
colours.  (137.)  These  first  precepts  may  serve  as  a  basis  for  the 
first  method  of  shading,  which  is  the  less  difficult  of  the  two  for 
beginners.  In  fact,  according  to  it,  the  graduated  shade  is  produced 
by  the  simple  superposition  of  a  number  of  flat  tints. 

FLAT-TINTED   SHADING, 

298.  Let  it  be  required  to  shade  a  prism,  A,  Plate  XVIL,  with 
flat  tints  : — 

According  to  the  position  of  this  prism,  with  reference  to  the 
plane  of  projection,  as  seen  in  fig.  1,  it  appears  that  the  face,  a'  b'i 
is  parallel  to  the  vertical  plane,  and  is  fully  illumined ;  it  should, 
consequently,  receive  a  clear  uniform  tint,  spread  over  it  by  the 
brush,  and  made  either  from  China  ink  or  sepia,  as  has  been  done 
upon  the  rectangle,  a,  b,  c,  d,  fig.  A.  When  the  surface  to  be 
washed  is  of  considerable  extent,  the  paper  should  first  be  prepared 
by  a  very  light  wash,  the  full  intensity  required  being  arrived  at  by 
a  second  or  third.  (137.) 

The  face,  V  g',  being  inclined  to  the  vertical  plane,  and  com- 
pletely in  the  shade,  should  receive  a  tint  (294)  deepest  at  the 
edge,  b  c,  and  gradually  less  intense  towards  g  h  ;  this  is  obtained 
by  laying  on  several  flat  shades,  each  of  different  extent.  For  this 
purpose,  and  to  proceed  in  a  regular  manner,  we  recommend  the 
student  to  divide  the  face,  V  g',  fig.  1,  into  several  equal  parts,  as 
in  the  points,  1',  2',  and  through  these  points  to  draw  lines  parallel 
to  the  sides,  b  c,  g  h,  fig.  A.  These  lines  should  bo  drawn  very 
lightly  indeed,  in  pencil,  as  they  are  merely  for  guides.  A  first 
greyish  tint  is  then  spread  over  the  surface  comprised  between  the 
first  line,  1 — -1,  and  tho  side,  b  c,  as  in  fig.  2;  when  this  is  quite 
dry,  a  second  like  it  is  laid  on,  covering  the  first,  and  extending 
from  the  side,  b  c,  to  the  line,  2 — 2.  as  in  fig.  3.  Finally,  these 
are  covered  with  a  third  wash,  as  in  liir.  A,  extending  to  the  outer 
edge,  g  h,  and  completing  the  graduated  shade  of  the  rectangle, 
b  r  g  h. 

The  number  of  washes  by  which  tin'  gradation  is  expressed, 
evidently  depends  upon  the  width  of  the  surface  to  be  shaded  ; 
and  it  will  be  seen  that  the  greater  the  number  of  washes  used, 


tho  lighter  they  should  be,  and  the  lines  produced  by  the  ed  •,  -  of 

each  will  he  less  hard,  and  a  more  beautiful  effect  will  result 

The  student  must  remember  to  efface  the  pencilled  guide-lines, 
as  soon  as  the  washes  are  sufficiently  dry. 

299.  This  method  of  overlaying  the  washes,  and  covering  a 
greater  extent  of  surface  at  each  succeeding  time,  is  preferable  to 
the  one  sometimes  adopted,  according  to  which  the  whole  surfaee, 
bg  h  c,  is  first  covered  by  a  uniform  wash;  a  second   h,  in 

laid  over  b  2—2  c;  and  finally,  a  third  over  the  narrow  strip, 
b  1 — 1  c.  When  the  shade  is  produced  in  this  manner,  theei 
the  washes  are  always  harder  than  when  the  washes  are  laid  on  as 
we  recommend — tho  narrowest  first — for  the  subsequent  washes, 
coming  over  the  edge  of  each  preceding  one,  soften  it  to  a  consi- 
derable extent. 

The  face,  e°  a1,  fig.  1,  being  likewise  inclined  to  the  vertical  plane, 
but  being  wholly  illumined,  should  receive  a  very  lighi  shade  I  392  ), 
being,  however,  a  little  holder  towards  the  outer  edge,  e  /',  fig,  A. 
The  shade  is  produced  in  the  same  way  as  that  of  the  face,  I  g  , 
but  with  much  fainter  washes. 

300.  Let  it  be  proposed  to  shade  a  cylinder,  fig.  [3,  with  a 
of  flat  tints  :— 

In  a  cylinder,  it  is  necessary  to  give  the  gradations  of  shade,  both 
of  the  illumined  and  of  the  non-illumined  portion.  In  reference  to 
this,  it  will  be  recollected  that  the  line  of  separation,  a  A,  of  fight 
and  shade,  is  determined  by  the  radius  inclined  at  an  angle  of  45°, 
as  o  a,  fig.  4,  perpendicular  to  the  ray  of  light;  consequently,  all 
the  shadow  proper,  which  is  apparent  in  the  vertical  projection,  fig, 
[§,  is  comprised  between  the  line,  a  b,  and  the  extreme  gen 
c  d.  Consequently,  according  to  the  principle  already  laid  down 
(296),  the  shade  of  this  portion  of  the  surface  should  he  graduated 
from  a  b  to  c  d,  as  was  the  case  with  the  inclined  plane  surface.  //  e '. 
fig.  1,  the  greater  intensity  being  towards  ah. 

On  the  other  hand,  all  that  part  of  the  cylinder  comprise  1  1„. 
tween  the  line,  a  b,  and  the  extreme  generatrix,  fg,  is  in  the  liglit : 
at  the  same  time,  from  its  rounded  form,  each  generatrix  is  at  a 
different  distance  from  the  vertical  plane  of  projection,  and  makes 
different  angles  with  the  ray  of  light.  Consequently,  this  portion 
of  the  surface  should  receive  graduated  shades.  (292.)  To  i 
the  effect  in  a  proper  manner,  it  is  necessary  to  know  what  pari  of 
the  surface  is  the  clearest  and  most  brilliant  ;  and  this  is  evidently 
the  part  about  the  generatrix,  e  i,  fig.  [IB,  situated  in  the  vertical 
plane  of  the  ray  of  light,  k  o,  fig.  4.  In  consequence,  In 
of  the  visual  rays  being  perpendicular  to  the  vertical  plane  and 
parallel  to  the  line,  v  o,  the  portion  which  appears  to  the  eye  to 
be  the  clearest  will  be  nearer  to  this  line,  v  o,  and  may  be  limited, 
on  the  one  hand,  by  the  line,  T  o,  bisecting  the  angle  made  by  the 
lines,  B  0  and  v  o,  and  on  the  other,  by  tin-  line,  K  o:  squaring 
over,  then,  the  points,  e1  and  m',  fig.  4.  and  drawing  the  lines,  t  i 
ami  hi  n,  fig.  3,  we  obtain  the  surface,  e  i  m  n,  which  is  the  most 
illumined. 

301.  This  surface  is  bright,  and  remains  white,  when  the  cylinder 
is  polished,  as  a  turned  iron  shaft,  for  example,  or  a  marble  column  ; 
it  is  covered  with  a  light  shade,  being  always  clearer,  however,  than 
tin'  rest  of  the  surface,  when  the  cylinder  is  unpoltt 

302.  Alter  these  preliminary  observations,  we  may  proceed  to 


the  i 


sttadr  the  ry«nu>r,  f  m'  «"  e*.  fig .  4,  dSridtng  il  int..  a  c-rUin  nun*- 
bar  of  eqaal  parts,  the  not  numerous  Meaning  m  the  cylinder  u 
|TMlif.  Tk.»din*.»iff  squared  over  to  the  vertical  projection, 
■ad  .traijfct  tnr.  drawn  H.+tly  witfc  the  pencil,  aa  limiting  guides 
fur  the  eoloor.  We  thro  lay  ■  fight  gray  ahade  on  the  surface, 
m  c  i  b,  fig.  5.  to  laiiiph*  at  once  the  put  in  tar  ahade ;  whea 
this  b  dry,  we  lay  oa  a  eeeood  covering,  the  fine,  a  k,  of  arparatinn 
of  light  and  ahade,  aad  extending  over  a  dhriaioa  oa  either  aide  of 
it,  aa  abown  in  fi,'.  6  .  we  afterward*  lay  oo  a  third  ahade,  covering 
two  divisions  to  the  right  aad  to  the  left,  aa  in  fig.  7  ;  and  proeeed 
at  the  seme  manner,  eorering  more  aad  more  each  time,  always 
keeping  to  Ate  pencil  lines.  IV  dflerent  stages  are  u  pi  eat  u  ted 
in  fig*.  8,  9,  and  10. 

,t  .hade  the  part,/?  i  g,  laying  on  antcaaaire  ahadea, 
bat  fighter  than  the  preceding,  as  indicated  in  figs.  S.  9,  and  10. 

Trio  operation  is  finally  terminated  by  laying  a  light  « 
the  whole,  leaving  untouched  only  a  very  small  portion  of  th< 
earftm,  e  at  a  i,  fig.  B-    This  last  wash  has  a  beautiful  and  i 

MIAMI.;    BT   SOfTEXED    U 

-torn  of  shading  differs  from  tho  former  in  pt 

.ht  and  >h:ui.    I 
by  manipulation  with  th<-  brush  in  U.  .r:  this 

system  possesses  the  adrantage  over  the  first,  of  not  leaving  any 
!.'■•«.  bMbbs*  :!.'■  bsssbTsbJ  aaasaaa  of  sssvJa,  wkkh  aonaetasss*.  ■•;•- 
pear  ban  .  and  seem  to  represent  facets  or  (lutings, 

- 
jchimry,  however,  the  former  «;.-' 
bringing  out  the  oljects  so  shaded  in  a  remarkable  manr 

.ail  machinery  to  be  sluuled  in  thai  manner, 
whilst  architectural  subjects  will  lo>  .1  according  to 

•bade  L«  miii  b  more  diffiou'v 
ing  considers!.  _•  in  the 

.'  systematic  course. 

-<  d  to  shade  a  truncated  hexagonal  pyramid, 
.  WII 

-  solid,  with  r  ■  •  vertical  plane 

of  projection,  i»  the  aame  aa  that  of  the  prism,  fig.  A-  Thus  the 
face,  abed,*!.  uniform  flat  a! 

rigorously  kee; 

■•■ttom,  aa  the  lace  is  not  quite  parallel   ' 
|>l.in«\ 
The  ' 

ply  a  first 

I  —  1.  as  a  limi 
this  »..ft.  run _-  i.  prod  ..-.  -i  '■■.  .  l.-arin^  the  braeh,  ■  •  thai  the  colour 

toe  aha.:  .)  be  taken  up  in  the  brush 

once  or  • 

being  t.  ,j  ^  out|jr,, 

abject, 


Wkn  this  first  wash  ia  w«D  dry.  a  second  is  laid  over  it.  produc- 
.  m  tin-  same  manner,  and  extending  further  to  the  right, 
covering  the  apace,  b  e  8 — A  aa  shown  ia  fig.  16.  Pi  mailing 
in  the  same  manner,  1-PfTnaig  to  the  Bomber  of  divisions  of  the 
fa  a,  asj  aj  '..  i  _-.:.  aaai  r  m*  ••>!.  •  ■:.-,  BfoaVjata|  aa  mmimtm  aaaaa, 
»g»cfig.  O. 

The  oprralions  are  the  same  for  the  tore,  «  a  a/,  which  b  nearly 
parpendicular  to  the  rays  of  fight,  bat  b  considerably  inclined  to  the 
a|aaj  ..t"  probtssom. 

on  this  face  should  be  gradua'  m  ef  to  a  J,  but  also 

(rum  r  a  to/  A  Abo,  on  the  face,  b  g  h  c,  in  the  shade,  the  tint 
should  be  a  trine  darker  at  the  base,  c  a.  being  graduated  off 
tow arda  b  g.     1  -so  simple  in  form  as  the  one  under 

considi  I  :y  may  be  neglected— at  any   rata,  by  the 

beginner— a-  only  increasing  hi*  difficulties  ;  the  proficiec'. 
other  It.  •  ,eee  refinement*  assists 

and  truthful  representations. 

.-  with  softened  waahea, 
\\VI1. 

■  the  indications  gi\.  •  ilar  im- 

-:.  jl.-s.  as  explained  with  reference  to  the  hat- wash 
sliading,  the  desired  effect  may  lie  similarly  pt 

-    irvcly  necos.tr  i  irrutn- 

many  ports  aa  I  I ;  a  first  shade 

Baa,  a  A,  of  separati  d  shade, 

and  th;-  ff  in  both  directions,  as  in  fig.  1 1  .  a 

. 
off,  and  in  this  manner  we  attain  th. 
13,  and  O. 
Wa  I  .1  it  nn  i  near)  -..ms  of  all  the 

preceding  cxai  ;racti*e  these  n 

.    rajsviiiy 

..!  can-.      If  they  i-rr  on  the  dark  aid 

• 

dry,  and  then  slightly  moarton 

i  a  clean  rag.     lighta 

taken   out   in    '  >  their  minuteness  or 

a  flat  ah 

"ff  tlie 
s-aah. 

- 
bave  already  been  discussed,  as  in-ti- 
cated  in  _  uidea,  also,  in  sharBno; 

with  w.i'  shades  in  that  pbte  are  pro- 

\  \\  II.  represent  the 
actual  appear .  -.i -shading  mei! 

Fina:  f  a  much  Urger 

..Me  to  produie  largo 
waahea  with  similarity  and  smoothness  of  I 


BOOK  OF  INDUSTRIAL  DESIGN. 


CONTINUATION  OF  THE  STUDY  OF  SHADOWS. 

Plate  XXVHL 

SHADOW   CAST   UPON   THE    INTERIOR   OF   A   CYLINDER. 

308.  When  a  hollow  cylinder,  as  a  steam-engine  cylinder,  a  cast- 
iron  column,  or  a  pipe,  is  cut  by  a  plane  passing  through  its  axis, 
we  have,  on  the  one  hand,  a  straight  projecting  edge,  and,  On  the 
other,  a  portion  of  one  of  the  ends,  which  cast  shadows  upon  the 
internal  surface  of  the  cylinder. 

We  propose,  then,  to  determine  the  form,  as  projected,  of  the 
shadow  cast  upon  its  interior  by  a  steam-engine  cylinder,  a,  sec- 
tioned by  a  plane  passing  through  its  axis,  figs.  1  and  1".  In  the 
first  place,  we  seek  the  position  of  the  shadow  cast  by  the  rectilinear 
projecting  edge,  B  c,  which  is,  in  fact,  produced  by  the  intersecting 
plane,  b'  a'.  This  straight  line,  B  c,  being  vertical,  is  projected 
horizontally  in  the  point,  b',  and  casts  a  shadow  upon  the  cylinder, 
as  represented  by  the  straight  line,  bf,  which  is  also  vertical,  and 
is  determined  by  the  point,  b  ,  of  intersection  of  the  ray  of  light, 
b'  4',  with  the  surface  of  the  cylinder,  b'  b'  o'.  Thus,  when  a 
straight  line  is  parallel  to  a  generatrix  of  the  cylinder,  the  shadow 
cast  by  it  will  be  a  straight  line  parallel  to  the  axis.  It  is,  therefore, 
evidently  quite  sufficient  to  find  a  single  point,  whence  the  entire 
shadow  may  be  derived. 

309.  We  next  proceed  to  determine  the  shadow  cast  upon  the 
interior  of  the  cylinder  by  the  circular  portion,  b'  e'  f',  of  the  upper 
end.  If  we  take  any  point,  e',  on  this  circle,  and  square  it  over  to 
E  in  the  vertical  projection,  and  draw  through  this  point  a  ray  of 
light,  e'  e',  e  e,  it  will  be  found  to  meet  the  cylindrical  surface  in 
the  point,  e',  which  is  squared  over  to  e,  the  length  of  the  ray  being 
equal  in  both  projections,  according  to  the  well  known  rule.  This 
applies  to  any  point  in  the  arc,  e'  f'.  The  extreme  point  on  one 
side  is  obtained  by  a  tangent  to  the  circle  in  the  point,  f',  giving 
the  point,  f,  in  the  vertical  projection ;  the  opposite  extreme  point, 
b,  being  already  given  as  the  top  point  of  the  straight  edge,  B  c ;  we 
have,  therefore,  the  curve,  Feb,  for  the  upper  outline  of  the  shadow 
due  to  the  circular  portion,  b'  e'  f'. 

310.  If,  as  in  figs.  1  and  I",  we  suppose  the  piston,  p,  with  its 
rod,  T,  to  be  retained  unsectioned  in  the  cylinder,  we  shall  have  to 
determine  the  form  of  the  shadow  cast  by  the  projecting  part  of 
the  piston  upon  the  interior  of  the  cylinder,  and  represented  by  the 
curve,  d  ho.  For  this  purpose  we  take  any  points,  b',  h',  o',  on  the 
circumference  of  the  piston,  and  draw  through  them,  in  both  pro- 
jections, the  rays  of  light  which  meet  the  surface  of  the  cylinder, 
b'  b'  o,  in  the  points,  V  h!  o',  which  are  projected  vertically  in  dho: 
the  curve  passing  through  these  points  is  the  outline  of  the  shadow 
sought.     The  curved  portions  of  these  shadows  are  elliptical. 

The  piston-rod,  T,  being  cylindrical  and  vertical,  casts  a  shadow, 
of  a  rectangular  form,  upon  the  interior  of  the  cylinder,  the  vertical 
sides,  if,  k  I,  being  determined  by  the  luminar  tangents,  i'  t',  k'  K, 
parallel  to  the  axis. 

SHADOW  CAST  BY  ONE  CYLINDER  UPON  ANOTHER. 

311.  Let  figs.  2  and  2*  be  the  projections  of  a  convex  semi- 


cylinder,  A,  tangential  to  a  concave  semicylinder,  B,  forming  a  pat- 
tern often  met  with  in  mouldings. 

This  problem,  which  consists  in  determining  the  shadow  proper 
of  a  convex  cylinder,  together  with  that  cast  by  it  upon  the  surface 
of  a  concave  cylinder,  in  addition  to  that  cast  by  the  latter  upon 
itself,  is  a  combination  of  the  cases  discussed  in  reference  to  figs.  4 
and  4*,  Plate  XXVI.,  and  to  figs.  1  and  1'  in  the  presenl  plate.  The 
operations  called  for  here  are  fulrj  indicated  nn  the  diagram;  and 
we  have  merely  to  remark,  that  it  is  always  well  to  start  by  deter- 
mining the  extreme  points,  as  c',  D,'  which  limit  the  shadow  propel 
c  g,  and  cast  shadow,  v>  c  g:  these  points  may  be  obtained  more 
exactly,  as  already  pointed  out,  by  drawing  the  radii,  o  c'  and  W  a, 
perpendicular  to  the  luminous  rays. 

shadows  of  cones. 

312.  In  this  branch  of  the  study,  we  propose  to  determine,  first, 
the  shadow  proper,  or  the  line  of  separation  of  light  and  shade  upon 
the  surface  of  the  cone  ;  second,  the  shadow  cast  by  the  cone  upon 
the  vertical  plane  of  projection;  and,  third,  the  shadow  cast  upon 
the  cone,  and  upon  the  vertical  plane  of  projection,  by  a  prism  of  a 
square  base,  placed  horizontally  over  the  cone. 

313.  First:  We  have  laid  it  down  as  a  general  principle,  that,  in 
order  to  determine  the  shadow  proper  of  any  surface,  it  is  necessary 
to  draw  a  series  of  parallel  luminous  rays  tangential  to  this  surface. 
When,  however,  the  body  is  a  solid  of  revolution  generated  by  a 
straight  line,  as  a  cylinder  or  a  cone,  it  is  sufficient  to  draw  tangen- 
tial planes  parallel  to  the  luminous  rays,  to  obtain  the  lines  of  sepa- 
ration of  light  and  shade. 

In  the  case  of  the  cone  represented  in  figs.  3  and  3%  and  of  which 
the  axis,  s  T,  is  vertical,  the  operation  consists  in  drawing  from  the, 
apex,  s  and  s',  two  lines,  making  angles  of  45",  as  s  s  and  s'  s\ 
giving,  in  the  point,  s',  the  shadow  cast  by  this  apex  upon  the  hori- 
zontal plane.  From  this  point  we  draw  a  straight  line,  a'  s',  tan- 
gential to  the  base,  a'  c'  b',  r.f  the  cone.  This  straight  line  repre- 
sents the  plane,  tangential  to  the  cone,  as  intersecting  the  horizontal 
plane  of  the  base;  and  the  contact  generatrix  is  then  obtained  by 
letting  fall  from  the  centre,  s',  a  radius,  s'  a',  perpendicular  to  the 
line,  a'  s' ;  and  this  line,  s'  a',  is  the  horizontal  projection  of 
the  lines  of  separation  of  light  and  shade.  The  vertical  pr- 
of this  straight  line  is  obtained  by  squaring  over  the  point  of  con- 
tact, a',  to  a,  and  then  drawing  the  straight  line,  s  a.  The  othei 
line,  s  b,  of  the  separation  of  light  and  shade,  is  similarly  obtained 
by  means  of  the  tangent,  s'  b'.  Its  vertical  projection  is,  however, 
not  apparent  in  fig.  3°. 

314.  Second:  The  shadow  cast  by  the  cone  upon  the  vertical 
plane  is  limited,  on  the  one  hand,  by  the  line  of  separation  of  light 
and  shade,  and,  on  the  other,  by  the  portion  of  the  illumined  base 
comprised  between  the  two  separation  lines.  Now.  the  straight 
line,  s  a,  casts  a  shadow,  represented  by  the  straight  line,  **  a',  as 
indicated  in  the  diagram  ;  and  the  base,  a'  e'  c'  b',  casts  a  shadow, 
represented  by  the  elliptic  curve,  fe  d  a',  which  is  determined  by 
points,  as  in  the  case  considered  in  reference  to  fig.  5,  Plate  XXVI. 

315.  Third:  The  shadow  cast  by  the  lower  side,  <;  it,  of  the 
rectangular  prism,  p,  upon  the  convex  surface  of  the  cone,  is  found 
in  accordance  with  the  principle  already  enunciated — that  when  a 
straight  line  is  parallel  to  a  plane  of  projection,  it  casts  a  shadow 


TIIK    I  <MAV8 


u;>  ■-,•'..»   |'.v  •.•■>■     \    •  n  SjajHBti  I     .   ^  -■-..  .'    IhM,  i-jua!  lad 
paralli  |  a  plan.-, 

M  V  parallel  to  iU  baar,  the  shadow 
upon  ti..«  pta:  1  by  drawing  from  t). 

ban,  itn  tad    ■;•  ■•-.  the  a\i-  ■  •!'  V.i-  rone,  sin!  projected  borizonUlly 
iaooi  ray.  which  nm  ti  this  pUm 
at,  t",  upon  Um 

'  draw  the  sir.  In-  tlu< 

sliadow  cut  I' 

rizontally  in  M 

!     ' 

_'tlt   lilH-, 

its  in  tlu-  outline  of  the  aha 
■ 

manner,  and  taking  »• 
•  m  r>,  any  number  of  point!  may  be 
obtaini-d.      It  ken  at  a 

..i^'lit  line,  i.  ii, 
this,  much  use- 
-     letermining  the  limiting 
•    before  us,  v. 

n  draw  a  luminous  ray.  and  ll 

of  the  eons,  it 
■quart- i 

W 
V,  of  the  same  shadow,  by  i  |nal  to 

I 
iminoui  ray,  a.s  situate,   in   a 

■ 
■ 

by  tlif  Imiiiii 
i  ind  drawn  through  the  points,  i  and  u,  in  the 

.  V,  tiii-  limit*  of  the  ennro  sought, 

-m.  r.  upon  tin-  virti.-.-i!  plai 
rity  apart  from  the  principles  alroad)  : 

SHADOW    or    ATI    IMVEBTED   COKE. 

31"     V. 

: 

ami  4*.  ' 

lined  by  draw. 
-    linen  at  an  ni. 

• 

I   be  observe- i 

I 
- 

The  ra-. 

rid  shnw  that  U  rti.m  of  tin   . 


the  sha 

less  than  that  ii  • ,  running 

- 
-ininates 
at  tin-  i 

. 
square  plinth,  I 

- 
•I".  i~  perpendicular  t-. 
- 

■ 

•1,  ami  than  drawing  through  the  |>oiiit,  o*,  the  straight  Ik 
paralU-l  to  the  ray  of  light,  as  in  Ihi  '  is,  at  sn 

boriaon;  nasi  draw  the  horisooUJ  D 
and  it  will  Im-  interaecti  >l  by  I 
which  is  consequent!) 

■ 
of  tin-  body  «'. 

cal  plain  .  in  which  tin-  ray  of  light  Ik  tgn  the 

point  whose  -  -lit  as 

• 
drill  U-  the  pi 

of  tin-  |>oillt. 

•  a  Irian- 

I    J 
then,  If  a  straight  lino 

;  by  tin-  luminous  ray, 
■ 

[f  ti,.  •  likewise  pass 

through  the  ufa 

wbothi  r  I  s  or  not,  an-l  th 

ral  projection  will,  in  I 

tin-  whl 

and  one  or  twi 
in  tin-  . 
oienl  let 
the  laminous  ray.  a- 

Aj    U  mil)  g,  of  the   ■ 

f  of  the  fruit 

■ 

at  iii  tin-  euro,  x*  f,  i<  a!V 


BOOK   OF    INDUSTRIAL   DESIGN. 


105 


by  means  of  (he  sectional  plane,  M  N  ;  G8  H,  fig.  4,  is  the  shadow  of 
the  edge,  g  h,  in  that  plane,  and  it  cuts  the  circle  representing  the 
section  of  the  cone  in  the  same  plane  in  the  point,  i",  which  is  ob- 
viously a  point  in  the  outline  of  the  shadow. 

SHADOW   CAST   UPON    THE    INTERIOR    OF    A   HOLLOW   CONE. 

318.  Fig.  5  represents  a  plan  of  a  hollow  truncated  cone,  and 
hi/.  5"  is  a  vertical  section  through  the  axis  of  the  object.  It  is 
required  to  determine  the  horizontal  projection  of  the  shadow  cast 
upon  the  internal  surface  of  the  cone  hy  the  portion  of  the  edge, 
a'  b  c,  and  the  vertical  projection  of  the  shadow  cast  by  the  sec- 
tional edge,  D  s,  and  by  the  small  circular  portion,  a'  d',  projected 
vertically  in  A  D. 

It  is  to  be  observed,  in  the  first  place,  that  the  straight  line,  D  s, 
which  is  a  generatrix  of  the  cone,  casts  a  shadow  upon  the  latter, 
in  the  form  of  a  straight  line,  for  the  plane  parallel  to  the  ray  of 
light,  and  passing  through  this  line,  D  s,  must  cut  the  cone  in  a 
generatrix  ;  we  therefore  draw  through  the  point,  d',  the  ray  of 
light,  d'  d',  making  an  angle  of  45°  with  the  base  line,  and  from 
the  centre,  s',  let  fall  the  perpendicular,  s'  e',  this  straight  line 
representing  the  horizontal  projection  of  the  intersection  of  the  cone 
by  the  plane  passing  through  the  line,  d'  s',  and  at  the  same  time 
parallel  to  the  ray  of  light.  By  squaring  over  the  point,  e',  to  e, 
fig.  5°,  and  joining  e  s,  we  have  the  vertical  projection  of  this  line 
of  intersection,  and  consequently  the  shadow  cast  by  the  line,  D  s. 
The  diagonal  ray  of  light,  d  d,  drawn  through  the  point,  D,  deter- 
mines the  limit,  d,  of  the  shadow.  The  horizontal  projection  of  the 
extreme  points,  a'  and  c,  of  the  curved  outline  of  the  shadow,  is 
also  obtained  by  means  of  the  tangents,  s'  a'  and  s'  c,  drawn  from 
the  point,  s,  in  which  the  ray  of  light  passing  through  the  apex 
intersects  the  plane  of  the  base  of  the  cone.  The  determination 
of  the  central  or  symmetrical  point,  b',  of  the  same  curve,  is  derived 
from  the  straight  line,  D  b,  drawn  from  the  point,  D,  parallel  to  the 
ray  of  light,  s  R",  as  in  the  diagonal  plane,  that  is,  as  at  s  R1 ;  the 
point,  b,  in  which  this  straight  line  meets  the  generatrix  directly 
opposite  to  that  passing  through  the  point,  D,  is  projected  horizon- 
tally in  the  point,  b',  upon  the  prolongation  of  the  diagonal  ray  of 
light,  s'  s'. 

319.  The  operation  for  finding  any  intermediate  point  in  the 
curve,  is  based  on  principles  already  explained  ;  namely,  that  when 

a  line  or  a  surface  is  parallel  to  a  plane,  the  shadow  cast  is  also  " 
a  line  or  a  surface  equal  and  parallel  to  the  first.  If,  then,  we 
draw  a  plane,  M  n,  parallel  to  the  base,  D  F,  of  the  cone,  the 
shadow  cast  by  this  base  upon  the  plane,  m  N,  will  be  a  circle  ;  it 
will  consequently  be  sufficient  to  draw  through  the  centre,  o,  fig. 
5°,  a  ray,  o  a,  which  will  meet  the  plane,  M  n,  in  a,  which  must 
be  squared  over  to  a',  on  the  horizontal  projection  of  the  same 
ray.  Next,  with  the  point,  a',  for  a  centre,  and  with  a  radius 
equal  to  D  o,  describe  a  circle,  h'ii;  this  will  represent  the  entire 
shadow  that  would  be  cast  by  the  base,  D  F,  of  the  cone  upon  the 
plane,  M  N  ;  this  plane,  however,  cuts  the  cone  in  the  circle,  of 
which  M  N  is  the  diameter  and  vertical  projection,  whilst  h'  m'  j  n' 
is  the  horizontal  projection  :  this  circle  is  cut  by  the  former  in  the 
points,  h'  and  j,  which  are  consequently  two  points  in  the  outline 
of  the  shadow  in  fig.  5,  and  the  one  of  these  which  is  seen  in  the 
vertical  projection  is  squared  over  to  ft,  upon  the  line,  H  N. 


AITLICATIONS. 

320.  In  this  plate,  as  well  as  in  Plate  XXVI.,  we  have  given 
shaded  and  finished  representations  of  several  objects,  which  servo 
as  applications  of  the  several  principles  we  have  just  pointed  Out, 
whether  referring  to  shadows  proper,  or  east,  or  to  graduated  shad- 
ing. Thus,  fig.  /&  represents  flu-  interior  of  a  steam-engine  cylinder 
with  piston  and  rod.  In  this  example,  regard  has  been  had  to  the 
general  principle,  that  shadows  are  the  stronger  the  brighter  the 
surfaces  on  which  they  fall  would  be,  if  illumined — that  is,  when 
such  surfaces  are  perpendicular  to  the  rays  of  light,  any  shadow 
cast  upon  them  will  be  most  intense  ;  the  shade  is  consequently 
made  deepest  about  the  generatrix,  corresponding  to  g  ft,  in  lig.  1 ', 
and  situate  in  the  vertical  plane  of  the  rays  of  light  passing  through 
the  axis  of  the  cylinder :  to  the  right  and  left  of  this  line,  the  shado 
is  softened  oft*. 

321.  In  the  graduation  of  the  shade,  regard  has  also  been  had 
to  the  effects  of  the  reflected  light,  which  prevents  a  surface  in  the 
shade  from  being  quite  black.  In  a  hollow  cylinder,  for  the  por- 
tion in  the  shade,  it  is  the  generatrix,  F  f",  fig.  1",  which  should 
receive  the  shade  of  least  intensity,  as  it  receives  the  reflected 
rays  of  light  more  directly.  It  will  he  recollected  that  the  point, 
f',  is  obtained  by  means  of  the  radius,  T  F',  perpendicular  to  the 
ray  of  light. 

Fi'T.  [g  represents  a  portion  of  a  common  moulding,  and  shows 
how  the  distinction  made  between  the  shadow  proper,  and  the  east, 
shadow,  tends  to  bring  out  and  show  the  form  of  the  object. 

Fig.  ©  is  an  architectural  fragment  from  the  Doric  order,  given 
as  an  application  of  shadows  cast  upon  cones,  as  well  as  those  cast 
by  cones  upon  a  vertical  plane. 

This  example  also  shows  how  necessary  it  is,  in  producing  an 
effectivs  representation  to  make  a  iiSirenc*  in  tin  intenai;  f 
shadows  cast  upon  planes  parallel  to  the  plane  of  projection,  and  at 
different  distances  from  the  eye;  and  also  to  give  gradations  to 
such  shadows  when  cast  upon  rounded  Burfaces. 

Fig.  ©  is  a  combination  of  a  cylinder  with  a  couple  of  cones, 
with  their  apices  in  opposite  directions,  showing  how  differently  the 
effects  of  light  and  shade  have  to  be  rendered  upon  each. 

There  is  less  shadow  upon  the  upper  cone  than  upon  the  cylin- 
der, whilst  there  is  more  upon  the  lower  cone  ;  the  reasons  of  those 
differences  have  already  been  explained  in  reference  to  tigs.  3" 
and  4". 

Fig.  g  represents  an  inverted  and  truncated  cone,  showing  the 
manner  of  shading  the  same,  and  the  form  of  the  shadow  cast  by 
me  square  tablet  above  ;  and  fig.  [Fis%aview  of  a  hollow  cone,  sec- 
tioned across  the  axis,  presenting  a  further  variety  of  combinations. 


TUSCAN    ORDER. 
Plate  XXIX. 
SHADOW    OF   THE    TORUS. 
322.  In  geometry,  the  torus  is  a  solid,  generated  by  a  circle,  re- 
viving about   an   axis,  continuing  constantly  in  the  plane  of  tins 
axis,  in  BUeh  a  manner,  that   all   sections   made    hy    planes   passing 
through  the  axis  are  equal  circles,  anil  all  sections  by  planes  perpen- 
dicular to  the  axis  will  also  be  circles,  but  of  variable  diameters. 


I 


Tim  rRuTH'M.  i 


.•  « .  n.  that  in  architecture,  the  torus  U  on. 
I/  p»ru  of  the  ba~ .  and  <•!"  the  racial  • 

■U  „•  das  -^-1  »■•  ^i-  ■  •!■  or  onnl  l>3  ■■■  >r>  "■'•  V*  'K,-,t  :':- !  ,:'  "'• 

.  in;,'  about  the 
t.al  sur- 

k    till'   |.rilH-i|«l 

Thus,  by 

. 

the  st-mkin  1.  «,  afc,  which  limit  the  contour  <.f  the  loroa  In  tho 

I 

Km  of  st-pora- 

. 

■ 
•!.•.. ntal,  b  f.  I':  ■•■  cune  will  be 

tdefa  will  lie  in  . 

:..  the  ray,  I 
■  the  torns,  in  the  point, 

I  \. rti.-.illy  in  tli.-  hori- 
zon Ul  li 
Ulil  tli  I" 

■ 
«nJ  wfa  in  the  rertieal  plane  pairing  tbroogh  the 

l — J,  we  pro- 
toned 

■ 
■ 

parallel  t"  tfai  i  ..l  piano, 

.1  is,  at  an  m 

ht     Hut   it   I. . 
tnuinf.  " 

..  r  t..  i*.  in  tl  I 

,-  i.  drawn  throngfa  i"1. 
I 
an.l  d,  in  the  eurred  I  •  but  H 

because  of  the  large  leala  of  tin-  drawing,  it  k  ■•■ 
be  done  bj  ■ 

aa  »'  a',  which 
in  a  da 

t,,  the  i  Plato  XXVI. ;  that  is 

to  say,  »c  seek  tli"  projection  "t  tli.-  Ituninoui  ray  npon  tl 

o'  a'.      I  lot   fall  u|xin  ,:  |.iiji.n. 

Inr.  «'  i  t  taken  upon  tin-  hnrinooa  ray,  • 

U  I  npon  the  pi 

'.  until  it 
idblg  with  r'.      Tln-n,  aa  tho 


!<•,  i-  i-,ua!  In 
that  of  the  point,  a,  tl  I  ..-#* uf 

.lid  tlie 
| 

ration.     If.  tin 

light  ainl  shade,  at  in  I  I 

.  in  n*. 
Lai,  n  n*, 
iwn  the 
■ 

which  v 
\ \\  I . ;  and  ■ 

in  l»>lh  cases. 
If  tin-  drenlar  an-  1m-  proton 
npon  it  . 

which  iaal 

the  luminous  ray.     '1.  .  in  tho 

.'.  drawn  at  a  • 
op, above  tin-  centre  line, //, equal  t->  t  -  .  uf  tho 

horizontal  paaalim  Ihrongh  the  point,  a*,  below  it. 

When  tin-  shadow  |  la  (a  known",  tl 

plane — the  plinth  or  | 

number  of  linea  parallel  to  tin-  luminous  ray.  an.l  then  fii 

i|-.>n  the 
I  which  la  a  cum-  ;  boil 
Hon, 

.  /■',  in  tlii->  curvi 

mi  from  the-  point,  /  /',  with  the  | 
*I"li.-  half  of  the  line  "f  separation  ■  ipon  tho 

il  portion  uft! 

n,  Is  similar  to  the  ai 

:i..n.f  J,  whDat 
■ 

rumounted  by  a  eyflndrieal  lilh-t,  tlm 

U f  separation  of  de  npon  the  latter  « 

the  t..ruv    Ti  I  -".  Una 

«i!l  be  the  case  with  the  Diet,  i>.  the  Due  ofaeparal 

Tl.ii  One,  I 
which  it  n  »tr:.  luminous  rs\ 

,t./.  a  luminous  ray.  I 
bortzontal  plane,  <i ./.  in  i,  which  |>--  otoj  t<« 

"the  horizontal  projection.    Il 
by  tin-  circular  portion./'^',  wkleh  i*  in  lb 
■ 

\  \  \  1  .        ■ 
i  v  of  the  ] 

iloation  ..f  tl..-  shadow,  nj,  ■ ' 
by  (he  cyllndl  npon  the  annular  got 

li  the  fillet,  l>. 


BOOK  OF  INDUSTRIAL  DESIGN. 


SHADOW   CAST   BY   A.  STRAIGHT   LINE    UPON    A   TORUS   OR 
,.,_  QUARTER-ROUND. 

■  326.  Fig.  3  represents  the  horizontal  projection,  as  seen  from 
below,  of  a  fragment  of  a  Tuscan  capital,  of  winch  fig.  3"  is  the 
vertical  projection,  the  object  of  these  figures  being  to  show  the 
form  of  the  shadow  cast  by  the  larmier,  F,  which  is  a  square  prism, 
upon  the  quarter-round,  A,  which  is  annular. 

We  yet  again  recall  the  general  principle,  that  when  a  straight 
line  is  parallel  to  a  plane,  its  shadow  upon  this  plane  is  a  straight 
line  parallel  to  itself.  For  the  rest,  it  will  be  sufficient  to  compare 
the  operations  indicated  with  those  of  figs.  3  and  3",  Plate  XXVIII., 
to  see  that  they  are  precisely  the  same :  thus,  on  the  onejiand,  we 
have  the  diagonal,  g/,  for  the  shadow  east  upon  the  quarter-round, 
where  it  is  limited  by  the  curve,  b  el,  the  line  of  separation  of  light 
and  shade  upon  this ;  and,  on  the  other  hand,  we  have  the  curve, 
i"  g  V,  likewise  limited  by  the  same  curve,  for  the  shadow  cast  by 
the  edge,  g  h,  of  the  larmier  upon  the  quarter-round. 

Figs.  3  and  3"  complete  what  refers  to  the  shadow  of  the  capital 
of  a  column  ;  they  show  the  operations  necessary  to  determine  the' 
shadow  cast  by  the  line  of  separation  of  light  and  shade  of  the 
quarter-round  upon  a  cylinder,  as  well  as  that  cast  on  the  same 
jylindef  by  a  portion  of  the  larmier.  The  operation,  in  fact,  simply 
consists  in  drawing  the  luminous  rays  through  various  points,  i"  e, 
in  a  portion  of  the  line  of  separation  of  light  and  shade  upon  the 
quarter-round,  finding  their  intersection  with  the  cylindrical  surface 
of  the  shaft,  e,  bymeans  of  the  horizontal  projection.  There  is 
no  peculiarity  or  difficulty  in  this  procedure,  and  the  whole  being 
fully  indicated  upon  the  diagrams,  we  need  not  pause  to  detail  it 
further. 

To  render  the  diagrams  just  discussed  more  generally  applicable 
tnd  intelligible,  we  have  not  given  to  the  different  parts  the  precise 
proportions  prescribed  by  this  or  that  architectural  order  ;  such  pro- 
portions, however,  will  be  found  in  fig.  &,,  which  represents  the 
model  fully  shaded  and  finished,  being  the  entablature  and  column 
vf  the  Tuscan  order.  A  double  object  is  intended  to  be  gained  by 
this  beautiful  example  of  drawing  ;  namely,  to  show  the  application 
of  the  principles  laid  down  regarding  shadows,  and  the  distinctness 
and  niceties  to  be  observed  in  the  various  intensities  of  the  washes, 
and  in  the  general  shading. 

SHADOWS   OF    SURFACES   OF    REVOLUTION. 

327.  It  will  be  recollected,  that  a  solid  or  surface  of  revolution 
is  that  which  may  be  said  to  be  generated  by  a  straight  or  curved 
line,  caused  to  turn  about  a  given  fixed  axis,  and  maintaining  a  uni- 
form distance  therefrom  ;  thus,  the  cylinder,  the  cone,  the  sphere, 
the  torus,  are  all  surfaces  of  revolution ;  so,  also,  is  the  surface 
generated  by  the  curve,  a  b  c,  revolving  about  the  axis,  a  b,  figs.  4 
and  4*.  It  follows,  from  the  above  definition,  that  every  section 
made  perpendicularly  to  the  axis  will  be  a  circle,  and  all  such  sec- 
tions wrill  be  parallel.  Every  section  made  by  a  plane  passing 
through  the  axis  will  give  an  outline  equal  to  the  generating  curve, 
and  which  may  be  termed  a  ?neridian. 

328.  The  shadow  of  a  surface  of  revolution  may  be  determined 
in  two  different  ways :  by  drawing  sectional  planes  perpendicular 
to  the  axis,  and  then  considering  the  sections  made  by  these 
plunes  as  bases  of  so  many  right  cones ;  or  by  imagining  a  series 


of  planes  passing  through  the  axis,  and  then  projecting  the  ray  of 
Ughl  Upon  these  planes,  so  as  to  draw  lines  tangential  to  (he  dif- 
ferent parts  of  the  outline,  and  parallel  to  the  projections 
ray  of  light,  the  points  of  contact  of  which  will  be  points  in  the 
line  of  separation  of  light  and  shade  sought.  This  latter  method 
having  been  applied  in  the  preceding  figs.  1  and  1",  Plate  XXIX., 
and  figs.  3  and  4,  Plate  XXVIII.,  we  deem  it  more  useful,  in  the 
present  instance,  to  explain  the  operations  called  fur  in  the  first 
method.  * 

Take,  then,  any  horizontal  plane,  b  d,  figs.  4  and  4',  cutting  the 
surface  of  revolution  in  a  circle,  the  radius  of  which  is  b  e,  and  tho 
horizontal  projection,  V  e!  d',  through  the  points,  b  and  d,  draw  a 
couplo  of  tangents  to  the  generating  curve  which  forms  tho  outline 
of  the  surface  of  revolution.  These  tangents  will  cut  each  other 
in  the  point,  s,  upon  tho  axis,  this  point  being  the  apex  of  an  im- 
aginary cone,  s  b  d;  through  this  apex  draw  a  luminous  ray,  s  / 
and  a'  b',  meeting  the  horizontal  plane  of  the  section,  b  df,\af,f; 
from  this  latter  point,  the  horizontal  projection,  draw  two  straight 
lines,/'  g1  and/'  i',  tangents  to  the  circle,  V  c  d' ;  then  the  points 
of  contact,  g'  and  i',  will  be  the  two  points  of  the  line  of  separa- 
tion of  light  and  shade  intersected  by  the  plane,  b  d,  and  they  are 
therefore  squared  over  to  the  vertical  projection,  fig.  4°,  i,  only 
being  there  visible. 

It  is  in  a  similar  manner  that  the  points,  h  and  j',  are  deter- 
mined, these  points  being  situated  in  planes,  c  d  and  E  F.  parallel 
to  the  first.  R  is  to  be  observed,  however,  that,  in  these  two  last 
cases,  the  imaginary  cones  will  be  inverted,  and  the  lumino 
must  consequently  be  drawn  to  the  left  instead  of  l"  the  right,  aa 
has  already  been  explained  in  reference  to  figs.  3*  and  4",  Plato 
XXVIII. 

329.  When  the  tangents  to  the  generating  curve  are  v< il 
is  the  ease  with  the  sectional  planes,  M  n  and  a  I.  the  points,  m  and 
n,  o&  the  line  of  separation  of  light  and  shade,  are  determined  by 
lines,  inclined  at  an  angle  of  45°,  and  tangential  to  the  circular  sec- 
tions in  the  horizontal  projection,  because  these  circular  sections  are 
the  bases  of  imaginary  cylinders  and  not  cones. 

When  a  sufficient  number  of  points  have  been  obtained  in  this 
manner,  as  in  fig.  4",  a  curved  line  is  drawn  through  them  all,  which 
will  'give  the  visible  portion,  m  i  n  hj  E,  of  the  line  of  separation 
of  light  and  shade  upon  the  surface  of  revolution.  This  method  is 
general,  and  may  be  applied  to  surfaces  of  revolution  of  any  outline 
whatever. 

As  it  is  w  ell  to  determine  directly  the  lowest  point,  /..  of  this  and 
similar  curves,  it  may  be  done  in  the  same  manner  as  for  the  torus' 
figs.  1  and  1",  namely,  by  drawing  the  ray  of  light,  r  b,  at  the  same 
inclination  to  tho  base  line,  as  it  is  in  the  diagonal  and  vertical 
plane,  and  then  drawing  parallel  to  it  a  tangent  to  the  outline  of 
the  surface  of  revolution,  the  projection  for  the  moment 
supposed  to  be  in  a  plane  parallel  to  the  ray  of  light,  r.'  a'  ;  th  • 
distance  of  the  point  of  contact,  A',  from  the  axis,  being  then  mea- 
sured upon  the  horizontal  projection,  r'  a',  of  the  luminous  ray 
oives  the  point,  k',  which  is  finally  squared  over  to  /..  in  the  hori- 
zontal line  in  the  vertical  projection  passing  through  the  same  point 
of  contact. 

A  portion  of  this  curve,  namely,  the  lower  part,  t.  k  j,  casts  a 
shadow  upon  the  cylindrical  fillet,  co;  to  determine  this  shadow 


1 1 


it  wffl.  u»  U*  fin4  |iar*.  be  ■in— iy  to  delaeati  the  boruoatal 
a   of  the  run  r.   il;.u>j   thro   to  draw    lumir 

t!ir-  a.*   •  *«•  or  two  p-  »nU   la  the 

thr  borUoetal  pr-^c. txm  of  the  filifl.     The   p..lDu  ia  ■ 

I— it  ami  rare  interwrt  lb*  rirrlr.  an-  thrr 

thr  vertical  pro)-rtioa  of  0»  ow  rare,  wheaee  i»  drrived  the 

:  f.     The  varioue  operation  Hue*  art  not  indicated  no  the 

1  coafaaioa,  bat  the  pmwxding  will  be  tmmij  eon. 


UO,  Pig.  4*  repreeenta  the  vertical  projection  of  a  bam*-. 
m  b  often  aeeo  in  balroniea  of  atone  or  marble,  and  eometimea 
ng  a*  an  avolated  standard,  or  a*  a  j 
!  ..an  annular  | 

aortace  of  aliirh  the  baae  of  the  fillrt  raaU  a  aha-: 
to  •»■<■  that  thai  ahado* 
a*  thow  occurring  la  fig*.  3  and  3*,  Plata   X\\  III  .  M  well  aa  in 

•■■.•'  •    • 

■ 
r.f  loiu.tir,  eoaaWag  of  aartaeea  of  revo  iti  W<    m  amend 

the  etodrnt  to  draw  them  upon  a  large  scale,  and  to  determine  the 
imtflne  of  the  ahadou  - 

which  we  have  laid  down.     Such  ba  -vie  of 

W 
-   .uppoeed  them  to  be  drawn  to  a  ».. 
ml  aiie. 

■ad  combinati 
wU  br  •  tuil  practice;  but  our  labour-,  would  ba 

ir.'.<  naiaable  wcrr  »c  to  give  them  all.    Our  exemplification*  involve 
aD  the  | 


\M>  PRACTICAL  DATA. 


fin*  dr-i 

:  ump*,  in  »li 
. 

.  \  I  \ 
III     l.il't  if  and /urn'itg  pvmpu,  in  which  l*.;!i  the  al«.%e  actiuna 
are  combined. 

:rt.ta. 

'■' 
- 

■ 

I 

-•■preeont  the 


.--■.■ 


the  diameter  of  the  piatoa,  and  P  for  the  weight  or  praam  »  oa  tat 
paaoa —  -* 


ipreaa  tbia  piiaaan  ia  powada,  it  most  ba 

.at  bring  the  weight  ia  pound,  of  a  cubic  foot  of 

formula  then  becomee— 

.,  D»  II 
P  ba* 

Bal  n,.  bbbuj  n,.  :.t  I.  .r  _•  .  \|*.  «-U  ■  f.-.t. 

333.  Independently  of  thia  load,  which  eorreapoada  to  the  ueeful 
•fleet  of  -the  machine,  the  power  an  '.ng  the  piatoa 

-  paaaire  reaiatancea  to  overcome,  n.. 

:1k-  pUtoo  against  the  aidea  of  the  pump. 
'  in  the  pipe*. 
3d.  The  n-lanlation  uf  the  water  in  its  peaaage  to  the  pump  by 

■ 
4th     .  live. 

Theae  reaiatancea  can  onh 

■I    d'AubUson,  that  the  load  to 
laJ  to 

II   •    1-08; 

■ 

l>-  II 
I •    -  -  '    •!  aud  r.-d. 

■ 

•  rmula, 

: t  /. 

icnuinrd   by  an   expression 

- 

i  of  thai 
.up. 

.  i  Iba.  to 
the  equ 

I 

•iiu. 

Mr*. 
335    W 

m  with 


BOOK   OF   INDUSTRIAL   DESIGN. 


ail  valves  having  a  great  body  of  water  above  them,  and  with  their 
uppeRsurfacc  greater  than  the  area  of  the  orifice  above. 

LIFTING   AND   FORCING    PUMPS. 

336.  A  pump  of  this  description  ordinarily  consists  of  a  cylinder 
with  a  short  suction  pipe,  a  discharge  pipe,  a  solid  piston,  termed  a 
plunger,  and  suction  and  discharge  valves. 

Two  such  pumps  are  frequently  coupled  together,  in  which  ease 
a  single  suction  and  discharge  pipe  serves  for  both. 

337.  The  power  necessary  to  work  one  or  more  pumps  is  ex- 
pressed by  52-5  D2  II  v,  or,  taking  into  account  the  force  necessary 
to  work  the  piston  by  itself,  557  D'Hi;  v  signifying  the  velocity 
in  fret  per  minute. 

This  velocity  is  obviously  obtained  by  multiplying  the  number 
of  strokes  per  minute  by  the  length  of  stroke ;  thus — 

v  =  2n  I, 
n  being  the  number  of  baek-and-fonvard  movements  per  minute  ; 
consequently,  the  power  required  is  equal  to 

55-7  D1  H  x  2nl  =  1114  DJ  H  n  I; 
this  product  representing  pounds  raised  one  foot  high  per  minute, 
the  measurements  being  in  feet. 

With  these  premises,  w7e  can  solve  such  problems  as  the  fol- 
lowing : — 

First :  What  force,  F,  is  required  to  work  a  pump,  having  a 
piston  6  inches  in  diameter,  a  stroke  of  18  inches,  and  a  velocity  of 
15  double-strokes  per  minute;  the  whole  height  between  the  well 
•  and  the  point  of  delivery  being  70  feet  ? 

The  velocity  v  =  2n  I  =  30  x  U  =  45  feet.  Then  F  =  557 
Da  x  H  x  v  =  55-7  X  -25  x  74  x  45  =  46,997  lbs.  raised  one 
foot  high  per  minute. 

To  express  this  in  horses  power,  we  must  simply  divide  it  by 
33,000 ;  therefore, 

_      46,997 

33  000  =  '  =  horses  power,  nearly. 

Second :  What  quantity  will  the  same  pump  raise  in  ten  hours  ] 
Assuming,  according  to  the  formula  (333),  the  effective  volume, 
V  =  -6  D2  I,  or  V='«x  -25  x  15  =  -225  cubic  feet  per 
stroke ; 
and  the  volume  per  minute, 

•225  x   15  =  3-375  cubic  feet ; 
and  per  hour, 

.    3-375  x  60  =  202-5  cubic  feet. 
The  quantity  of  water  raised  in  ten  hours  will  consequently  be 
202-5  X  10  =  2,025  cubic  feet. 
Third:  What  diameter  should  be  given  to  the  piston  of  a  pump 
which  raises  202-5  cubic  feet  of  water  per  hour,  the  velocity  being 
45  feet  per  minute,  the  length  of  stroke  18  inches,  and  the  height 
to  which  the  water  is  raised  75  feet? 

The  formula  above,  relative  to  the  effective  discharge  per  stroke, 
V=-6D'  x  /, 
by  transposition,  becomes 

D^nrx-r 

Now,  the  volume,  202-5  cubic  feet,  discharged  per  hour,  is,  per 

minute,  20-2-5 

-  60    =  3375  cubic  feet. 


This  hist  again  reduces  itself  to 
2  x  1-5  x  3-375 


225  cubic  feet  per  stroke; 


consequently, 


D'  = 


Whence, 


D=V/-JxV5  = 


6  inches. 


THE    HYDF.OSTATIC   PRESS. 

338.  This  powerful  machine  is  an  application  of  the  lifting  and 
forcing  pump.  It  consists  of  a  bulky  piston,  or  plunger,  termed  a 
ram,  working  in  a  cylinder  to  correspond,  and  communicating,  by  a 
pipe  of  small  bore,  with  a  small  but  very  strong  forcing  pump. 
To  the  top  of  the  large  piston  is  fixed  a  table  or  platform,  which 
compresses  or  crushes  what  is  submitted  to  the  action  of  the 
machine. 

The  pressure  exerted  upon  the  water  by  the  smaller  piston,  is, 
by  means  of  the  fluid  contained  in  the  pipe,  transmitted  to  the  base 
of  the  ram;  and  as,  according  to  the  well-known  hydrostatic  law, 
the  pressure  is  equal  on  all  points,  the  total  force  acting  on  each 
piston  will  be  in  proportion  to  their  area ;  so  that  if,  for  example, 
the  diameters  of  the  pistons  are  to  each  other  as  1  to  5,  the  pres- 
sure on  the  larger  one,  the  ram,  will  be  25  times  as  great  as  that 
exerted  by  the  pump-piston.  Suppose  a  man  can  apply  a  force 
equal  to  60  lbs.  to  the  end  of  a  lever  3  feet  long,  and  that  the  point 
of  connection  with  the  piston-rod  is  only'li  inch  from  the  fulcrum, 
the  leverage  of  the  power  will  be  24  times  as  great  as  that  of  the 
resistance,  and  the  pressure  upon  the  ram  will  consequently  be 
24  x  25  x  60  =  36,000  lbs.,  an  effort  equal  to  that  of  600  men 
acting  at  once. 

In  the  hydrostatic  press,  we  have,  consequently,  to  consider  two 
mechanical  advantages — that  of  the  simple  machine,  the  lever,  and 
that  of  the  ram :  these  advantages  are,  however,  necessarily  com- 
pensated for  by  the  diminution  in  the  velocity  of  the  ram. 

On  these  principles,  enormously  powerful  presses  and  lifting- 
machines  have  been  constructed.  The  one  capable  of  lilting  18,000 
tons,  at  the  Menai  Tubular  Bridge,  is  an  unparalleled  example. 

HYDROSTATICAL    CALCULATIONS   AND   DATA — DISCHARGE   OF 
WATER   THROUGH   DIFFERENT   ORD7ICES. 

339.  The  discharge  of  a  volume  of  water,  in  a  given  time,  varies 
according  to  the  velocity  of  the  water,  and  depends  upon  the  area 
and  form  of  the  discharge  orifice. 

Surface  Velocity. — The  velocity  of  water  at  the  surface  of  a  water- 
course or  river,  of  which  it  is  wished  to  ascertain  the  discharge,  is 
obtained  by  means  of  a  float,  which  is  thrown  into  the  part  where 
the  current  is  strongest.  As  the  wind,  if  there  is  any,  affects  the 
result  very  considerably,  the  float  must  project  above  the  surface  as 
little  as  possible.  A  distance  of  as  great  a  length  as  convenient  is 
measured  on  the  part  of  the  stream  where  the  current  is  most  regu- 
lar, and  the  time  occupied  by  the  float  in  passing  that  distance  is 
noted  by  a  seconds  watch.  The  space  passed  through  is  then  divided 
by  the  time  expressed  in  seconds,  and  the  quotient  will  be  the  sur. 
face  velocity  per  second. 


Tin:  i 


•aaJ  U>  try  aeveral  fl  *U  in  diftntl  perta  of  the  runroL 
/  -ore  pwacd  through  by  each  float  is 

.3  ij  «v  «oJ> 

\ 

If  the  velority  i<  not  uniform  throw  fth  of  the  canal, 

mr  point  du  ■  *nul" 

padJl^wnwI.  the  IwU  uf  which  ju«t  <ii|>  into  the  water.     The 

•   thin  iiintnirncnt  tK-ii 
plani  by  it»  moan  rircumfiTei 

[»■«**»«;  |o  the  centra  of  the  unmerf*ed  part  of  the  tl  ..it — 1 1 1 ■  -  pro* 
dart  npn —  - 
• 
/ 

jihI  tliat  tin-  i  ll  to  IJfoOt,  wh.it 

i«  the  aur'  UTOOt! 

VI.  •;!>•  tliat 

irhola  body  of 

•    I w  for  Iha  ganging  .if  lha 

dplying  it  by  n 
coefficient,  wl 


Tm  m  •  ■■ 

•  ( iftj  !• 
of  V    U. 


/  ity  of  a  current  of  which  the 

I-     .    , .  •     88  x  S      1*10  mat 

Tlir  i  'i»  »"  Op«l  mtatvoOtUM  or  river  of 

■;.  tin-  following  formula: — 

/A       II 
V*  =  66  86  x  \/ 

V   V        I. 

■  hudnmtnt  of  lha  exact  level  of  tha 

aurfare  I  iter  lha 

■ 

lit  of  lha  GUI,  II  dot- 
•li,  L 
/  •  tha  irate  in  ■  wate- 

.i  width  of  •(■'> 

■ 

•^MHvtioruil  area.  A, 

=  35  X  li  =  43ii 

r. 

■ 

-oTft       -8 

V  =  56B6>  \  ,  ,_    ,    -  -30  =  339 

i  una  formula,  it  n  neoeaaary  ao  aartnol  lha 

I  under  lha  rmli- 
.  ■  multiply  thia  root  by  th«  co-efficient  58  88 ; 


and.  finally,  to  auolmct  from  the  p* 

i  are  iii  > 


kiaoa  or  rur.v  ii   av 

•  ■•jii.nl    to  a  cubic   Dl 

1 1 '  -99-29  litre-  or  cubic 
Tin  aw  aECTtOH 

AMi    ! 

:ui.  w 

inlform  fall,  tli. 

ruiiiln  : — D  =  A   X   V  ,  in   v.  h 

\  1   area 

<  ity. 
/  V* 

■       .  and  the  mean 
D      u  ■  1*065  s-  4*478  eabie  in.ir.-,  or  4-478  litre-  par  aacond 

IV    AT    THE    BOTTOM    ' 

849.  Tin-  velocity  ■•('  irate  at  the  bottom  of  water-couraea  b> 

■  t > i -•  1 1  the  mean  *i  loclty. 
Pntfit     \  .ist  the  -uri'aee  velocity,  \   me  moai 

eity,  ati.l  \"  the  ground  velocity,  (he  relation  of  the  three  will  !•« 
erraoaaod  by  V"      8  V —  V.    Hud  i-  to  -ay.  tha  vebcil 
bottom  •  ,  i.il  t"  twice  lha  moan  velocity  minna  tho 

aarfaoa  velocity. 

/  1  rdodty  of  a  wate-way  at  found  to  be 

■  .  ami  the  mean  relodty  calculated  t 
la  the  ground  velocity  I 

V*  =  a  x  1-55  —  2=  110  i 
l  ■  velocity  at  the  bottom  of  a  water-eouraa  leoda  bo 

nd  carry' aw  ay  the  bed,  millennium:.'  Ihe  -i'b-  ami  OBaabjg 

deal  of  damage;  too  -mall  a  velocity,  on  the  other  hand,  by 
allowing  the  matter  raapandad  in  the  water  to  aettli 

1 

The  following  (able  ahowa  the  limit  of  velocity  aooorani  • 
al  the  bed,  which  eannot  be  exoeeded  without  danger: — 


N.lurr 


Limit  of  tllP  Vrlerit  jf  per  tocond. 


Ih 











Rock   friiL'm. nt« 

N.h.l  ro.k 


313.    /'  T'.e   prodooa  "I"  any   -niree  may  alao 

Bred  by  ilaiiiiiiim..'  up  the  entire  width  of  the   -Iream   with 
thin   pi.. 

no,    Tboaa  ' 

•ii.  until  the  level  of  the  water  within  them 


BOOK  OF   INDUSTRIAL   DESIGN. 


is  maintained  above  their  centres ;  so  that  when  this  is  affected, 
the  discharge  is  calculated  from  the  number  of  orifices  which 
require  to  be  open. 

The  quantity  of  water  discharged  by  each  orifice  of  '02  m.  in 
diameter,  in  a  board  -017  m.  thick,  and  under  a  column  -03  m. 
e  the  centre,  is  20  cubic  metres  in  24  hours. 

Another  method  of  gauging  a  stream  of  water,  consists  in  setting 
up  an  under  or  overshot  sluice-gate  at  a  similar  dam,  the  discharge 
being  calculated  according  to  the  following  rules  in  refereneo  to 
this  subject : — 


CALCULATION   OF   THE   DISCHARGE    OF    WATER    THROUGH 
RECTANGULAR    ORIFICES   OF   NARROW   EDGES. 

344.  As  it  is  of  importance,  in  a  majority  of  circumstances,  to  bo 
able  to  calculate  the  discharge  of  water  by  sluice-gates,  or  by  tlio 
vertical  discharge-gates  of  hydraulic  motors,  so  as  to  know  the 
volume,  and,  consequently,  the  value  of  a  stream  of  Water,  We  shall 
commence  by  giving  a  table,  which  enables  us  to  determine  this 
discharge  in  a  very  simple  manner,  and  places  these  operations 
within  the  capacity  even  of  labourers  and  working  mechanics. 


TABLE    OF   THE    DISCHARGES   OF    WATER    THROUGH   AN  ORIFICE    ONE    METRE    IN   WIDTH. 


Height 

of  the 

Volume  discharged  in 

itres  per 

second,  co 

responding  to  the  b 

eights:— 

metres. 

•2  m. 

■3  m. 

•4  m. 

■5  m. 

'6  m 

•7  m. 

•8  m. 

10  m. 

1-2  m. 

|l,m. 

1'fn. 

1-8  m. 

2  0  m. 

2  5  m. 

3'0  m. 

3-5  m. 

40  m. 

4 

50 

61 

71 

79 

86 

93 

99 

110 

121 

130 

138 

146 

154 

172 

188 

201 

215 

5 

62 

76 

88 

98 

107 

116 

124 

138 

151 

162 

173 

182 

191 

214 

255 

251 

268 

6 

75 

91 

107 

117 

128 

139 

148 

165 

181 

194 

207 

218 

229 

257 

281 

301 

321 

7 

86 

106 

122 

136 

148 

161 

172 

192 

210 

226 

241 

255 

267 

299 

327 

350 

374 

8 

98 

120 

139 

155 

170 

184 

196 

219 

240 

258 

275 

290 

305 

341 

374 

400 

427 

9 

109 

135 

156 

174 

191 

208 

220 

246 

267 

289 

309 

326 

343 

382 

420 

450 

481 

10 

122 

149 

173 

193 

212 

228 

246 

272 

298 

321 

342 

362 

380 

424 

466 

500 

533 

11 

133 

161 

189 

212 

230 

249 

267 

299 

327 

353 

376 

398 

418 

466 

511 

550 

587 

12 

145 

178 

206 

230 

251 

272 

291 

321) 

356 

384 

409 

434 

455 

507 

557 

599 

640 

13 

157 

192 

222 

249 

272 

294 

314 

352 

385 

416 

443 

469 

492 

549 

602 

647 

693 

14 

168 

206 

238 

267 

292 

316 

338 

379 

414 

446 

476 

504 

530 

590 

648 

697 

715 

15 

179 

220 

255 

285 

312 

338 

361 

405 

443 

477 

509 

539 

566 

631 

693 

747 

7 '.Hi 

16 

190 

,234 

271 

304 

330 

360 

385 

432 

472 

509 

542 

574 

603 

673 

739 

797 

852 

17 

201 

248 

2S7 

322 

350 

382 

414 

456 

501 

540 

575 

610 

638 

715 

784 

847 

905 

18 

213 

262 

304 

340 

370 

403 

432 

484 

529 

571 

608 

644 

677 

757 

830 

896 

958 

19 

223 

276 

324 

358 

392 

425 

454 

510 

558 

601 

641 

680 

715 

799 

876 

946 

1011 

20 

235 

29] 

3£7 

377 

414 

447 

485 

536 

586 

627 

675 

715 

753 

841 

922 

996 

1Q66 

21 

247 

305 

354 

396 

431 

470 

512 

563 

615 

664 

708 

751 

790 

884 

96  ! 

1046 

1118 

22 

259 

320 

370 

417 

451 

492 

538 

590 

645 

695 

742 

787 

828 

926 

1014 

1096 

U71 

23 

271 

334 

388 

434 

472 

515 

550 

616 

674 

726 

776 

823 

865 

968 

1060 

1146 

1 22 1 

24 

282 

348 

404 

452 

492 

537 

574 

643 

703 

758 

809 

859 

903 

1010 

1 106 

1 195 

1278 

25 

294 

363 

420 

471 

516 

559 

598 

670 

733 

790 

843 

895 

911 

1052 

1  152 

1215 

1331 

26 

306 

377 

437 

490 

538 

581 

626 

697 

762 

822 

877 

930 

978 

1094 

1 198 

1295 

1 38  1 

27 

318 

392 

454 

509 

559 

604 

645 

724 

791 

853 

911 

966 

1016 

1136 

12  15 

1345 

1437 

28 

329 

406 

471 

527 

573 

626 

679 

740 

820 

885 

914 

1001 

1 05  1 

1172 

1291 

1395 

1  191 

29 

340 

421 

487 

546 

602 

649 

693 

777 

850 

916 

978 

1037 

1092 

1220 

1337 

14  14 

15  14 

30 

353 

434 

504 

564 

624 

670 

718 

804 

880 

948 

1010 

1073 

1129 

1262 

1385 

1  194 

15: 17 

31 

364 

449 

521 

583 

635- 

694 

741 

831 

909 

980 

1046 

1109 

1167 

1305 

1  129 

1544 

1650 

32 

376 

463 

538 

602 

655 

715 

765 

857 

939 

1011 

1079 

1144 

1205 

1366 

1  175 

1594 

17113 

33 

388 

477 

555 

622 

676 

737 

789 

884 

969 

1043 

1113 

1180 

12  12 

1389 

1521 

164  l 

1756 

34 

400 

491 

572 

640 

696 

759 

813 

911 

998 

1074 

1147 

1216 

1279 

1431 

1568 

1693 

1810 

35 

415 

507 

588 

659 

717 

782 

837 

938 

1027 

1103 

1180 

1252 

1317 

1473 

1614 

1743 

1863 

36 

424 

520 

605 

677 

737 

804 

861 

965 

1057 

1138 

1214 

1288 

1355 

1515 

1660 

17:  i:; 

1916 

37 

436 

534 

622 

696 

758 

826 

885 

981 

1086 

1169 

1248 

1324 

1392 

1557 

1706 

1843 

I96g 

38 

450 

549 

638 

715 

778 

849 

909 

1018 

1115 

1201 

1283 

1359 

1430 

1599 

1 752 

1893 

2023 

39 

462' 

564 

653 

734 

798 

872 

933 

1045 

1145 

1232 

1315 

1395 

1  168 

16U. 

1798 

1943 

2U76 

40 

484 

577 

671 

753 

819 

894 

957 

1070 

1174 

1266 

1351 

1431 

1506 

1683 

1844 

1992 

2129 

41 

.. 

591 

688 

772 

840 

915 

981 

1097 

1203 

1298 

1384 

1467 

1543 

1725 

1890 

2012 

2182 

42 

. 

606 

705 

790 

860 

936 

1005 

1124 

1233 

1329 

1419 

1503 

1581 

1768 

1936 

2092 

2236 

43 

, 

620 

722 

809 

881 

961 

1028 

1151 

1262 

1361 

1453 

1538 

1618 

1809 

1982 

2142 

2289 

44 

, 

635 

737 

828 

901 

983 

1053 

1171 

1291 

1393 

1486 

1574 

1656 

1851 

2029 

2192 

2343 

45 

, 

649 

754 

847 

920 

1005 

1076 

1204 

1321 

1424 

1520 

1609' 

1694 

1894 

2075 

2241 

2394 

46 

, 

663 

771 

866 

941 

1028 

1100 

1231 

1350 

1456 

1554 

1636 

1731 

1936 

2121 

2291 

2  1  19 

47 

. 

677 

787 

885 

961 

1050 

1124 

1257 

1380 

1488 

1588 

1681 

1769 

1978 

2167 

2341 

2504 

48 

. 

691 

801 

903 

982 

1072 

1148 

1284 

1409 

1519 

1622 

1716 

1807 

2020 

2213 

2391 

3659 

49 

, 

706 

820 

922 

1002 

1095 

1172 

1311 

1438 

1551 

1656 

1753 

1845 

2062 

23.-S!! 

2440 

261  1 

50 

' 

719 

B36 

940 

1023 

1115 

1194 

1337 

1468 

1583 

16!  HI 

1789 

1882 

2104 

2395 

2490 

2669 

Tin:  i'K\<  : 


TNa  Ubic  hm  bran  calculated  by  m«n»  of  tli< 

I»    -  rk  x    ♦'StfH  x  1000; 
n  which 

•  volume  of  wat.-r  divlurptl  in  litres  per  ■ 
toatreo; 

;.rcwitiro,  in  mrtre«,  measured 
•     ■  f  lln-  rv- 

>  1 1  US) ;  sn-l, 

m  ii  a  i 

*  ai 

..11  four 
nJc- 

'  imn  of  tin*  table  wo  pive  tin 
and  in  the  following  columns:  the  n  raid  of  8m  >li~ 
chsrge  effected,  in  III  -  of  the 

I 

•  in  now  ilit<rtnim\  by  I  W  r . 

:  through  a  vortical  Bood- 

•  orifice,  of  which  thi 

■  the  top  of  the  orifice, 
\V.  bare,  in  I'.i.  t.  aimply  \»  find  the 

and  to  the  cnlumn  ••/  ir-  El  centre,  and  lluii  mullijily  this 

I  ■  .1  by  the  orifice 

.:  of  the  orifice 

•  i  ihc  column,  from  t li •-  centre  of  the 

rvoir,  8*6  m.,  and  the  oontrso- 
■ 
In  tin  Una  with  (he  I  nitres,  and  la 

.  will  be  found  the  number 

•  r  the  actual  d  GOod, 

It  will  !«•  equally  i 

h  ii"  not  happen  i"  !»• 

II  ed  by  :i 
-  m.  In  width,  the  height  "f  Ll 

H  tnn  ii |~ -ii  the  centre  i  ' 

not  in  the  table,  bul 

itiy,  the 
for  I  ■     ' 

!  ii  will  be  about  706;  therefore  the 

I 

\- 
■  In-  dia- 
the  numbers  '  : 

M    Ilillll- 


■ 
■ 

•i  of  the  aidea  of  the  reservoir 

- 
In  tlii*  ease,  in   order  t"  cslculati 
moat  In-  multiplied  by 
1*126,  If  the  contraction  la 

" 

/  I  the  volume  "f  water  diacharged  I  . 

height,  1*1  in.  in  width,  and  «iih  a  eolnma 
•  I  fri'in  the  centre  of  the  orifice,  the  bottom 
.  ■  line  with  the  bottom  of  the  reservoir;  i! 
■  on  taking  place  only  <>n  the  I 
It  will  !»■  found, according  t"  the  table,  thai 

Ires  for  a  width  of  one  metre,  and  consequently  098  •    I  i 
=  777  litres,  is  the  dit  I   .in.,  when  the  contraction  is 

i iplete.    We  have,  then  R        7TJ       I 

actual  discharge  sought. 

— Ii  mtv  often  bappaaa  that  tlio 
sluicegate  i*  Inclined.    In  thii  case,  If  there  i-  no  contraction  <>n  tlio 

to  !»•  oonaklera. 
1.1  v  augmented.    'Ilui".  to  calculate  the  effective  diachai 

\  to  multiply  tin-  numbera  in  the  pri 
If  the  sluice  ia  inclined  i  «itli  l  main 

u<  l  in  hi  ight  and  bj  1*23,  it  the  inclination  ia  60  ,  <t  l  n  i 
3  in  lii  ight 
/  |  know  the  vblui 

through  an  orifice  inelinod  at  an  angle  of  41  .  having  1"  m.  in 
liii^-lii  vi  rtically,  1*21  m.  in  width, and  at  ■  d  a  below 

voir;  the  !«•• 
being  in  :i  line  «iili  the  »idi  -  of  the  n  - 

Fn.in  the  tabl 
dischsrge  %<> i 1 1 ■  a  vertical  ortfiee  ;uul  eompli 
quently,  I  "ill  1"'  il»'  effective  di 

sought, 

:i  n.  When  vertical  il I  rati  -  have  tlnir  lower  •  I 

the  bottom  of  the  reservoir,  at  hi  general!)  the  oa*  .  t"  di  termlne 
the  dim  i 

M       ,lii  the  number*  xiirn  in  tht  tmble  by  1*04. 
/ 

orifice  of  which  is  opened  to  ■  hi 
8  in.  in  width,  and  -  •'<  n.  1*  lag  the  distance  from  thi 
I.,  the  upper  Ii 

10  litrsa  for  tin 
■■.in  width.    Whence  1,698  x  *8  x  1*04 
ought 

not  mora  titan  three  n 
h  other,  and  i  ifja  ■■'" 

Ik-  nlilaiiH  •!  1  ■>' 


BOOK  OF  INDUSTRIAL  DESIGN. 


Multiplying  the  numbers  given  in  (he  table  by  '915. 
Example. — If  the  orifices  of  two  sluices,  situated  at  a  couple  of 
metres  distance  from  each  other,  have  together  a  width  equal  to 
1-5  m.,  and  are  both  opened  to  a  height  of  -45  m.,  the  column  of 


water  upon  their  centres  being  1-8  m.,  what  will  be  the  effective' 
discharge  of  the  two  together  per  second? 

In  the  table,  we  find  that  1609  litres  corresponds  to  a  column 
of  1-8  m.,  and  a  width  of  1  m.  Therefore,  1609  x  15  x  915 
=  2208-35  litres  is  the  required  discharge. 


TABLE  OF  THE  DISCHARGE  OF  WATER   BY   OVERSHOT  OUTLETS   OF  ONE  METRE  IN  WIDTH. 


Heishts 
of  the 

Discharge 

Heights 
of  the 

Disc 

n"'6 

Heights 

of  the 

Discharge 

the  bottom 
of  the  outlet. 

litres  per  second. 

level  above 

litres  pe 

r  second. 

level  above 

litres  per  second. 

1st  Case. 

2d  Case. 

the  bottom 
of  the  outlet. 

1st  Case. 

2d  Case. 

the  bottom 
of  the  outlet. 

1st  Case, 

2d  Case. 

5-0 

20 

21 

28-5 

259 

283 

52-0 

639 

698 

5-5 

23 

24 

29-0 

266 

290 

52-5 

648 

708 

60 

26 

27 

295 

273 

298 

530 

658 

718 

6-5 

29 

31 

30-0 

280 

306 

53-5 

667 

728 

7-0 

32 

34 

30-5 

287 

313 

54-0 

676 

738 

7-5 

36 

38 

31-0 

293 

321 

54-5 

685 

748 

8-0 

40 

42 

31-5 

301 

329 

55-0 

694 

758 

8-5 

43 

46 

32-0 

309 

337 

555 

704 

769 

90 

47 

50 

32-5 

315 

344 

560 

713 

779 

95 

51 

54 

330 

323 

353 

56-5 

72  1 

790 

"    10-0 

56 

59 

33-5 

330 

361 

57-0 

733 

800 

105 

60 

63 

34-0 

338 

369 

57-5 

743 

811 

11-0 

64 

68 

34-5 

345 

377 

580 

753 

822 

11-5 

68 

73 

350 

353 

385 

58-5 

762 

832 

12-0 

72 

77 

35'5 

360 

393 

59-0 

771 

842 

12-5 

.77 

82 

36-0 

368 

402 

59-5 

781 

853 

130 

82 

87 

36-5 

375 

410 

600 

791 

864 

135 

86 

92 

37-0 

382 

419 

60-5 

801 

875 

14-0 

92 

98 

37-5 

392 

428 

61-0 

811 

886 

14-5 

97 

103 

38-0 

399 

436 

61-5 

821 

896 

150 

101 

108 

38-5 

408 

445 

62-0 

831 

907 

15-5 

107 

114 

390 

415 

453 

62-5 

811 

918 

160 

111 

119 

39-5 

423 

462 

630 

851 

929 

16-5 

117 

125 

40-0 

431 

471 

635 

861 

940 

17-0 

121 

130 

40-5 

439 

479 

64-0 

871 

951 

17-5 

127 

136 

41-0 

447 

488 

645 

882 

963 

180 

132 

142 

415 

455 

497 

650 

892 

974 

18-5 

138 

148 

42-0 

463 

506 

65-5 

902 

985 

190 

143 

154 

42-5 

472 

515 

66-0 

912 

996 

195 

149 

160 

43-0 

481 

525 

66-5 

922 

1007 

20-0 

154 

166 

43-5 

488 

533 

67-0 

932 

1018 

20-5 

160 

173 

44-0 

497 

543 

67-5 

943 

1030 

21-0 

166 

179 

44-5 

506 

552 

68-0 

954 

1042 

21-5 

171 

185 

45-0 

514 

561 

68-5 

965 

1054 

22-0 

176 

192 

45-5 

523 

571 

69-0 

976 

1066 

22-5 

182 

199 

46-0 

531 

581 

695 

*    987 

1078 

23-0 

188 

205 

465 

540 

590 

70-0 

998 

1090 

23-5 

194 

212 

47-0 

549 

599 

70-5 

1008 

1101 

240 

202 

219 

47-5 

•    558 

609 

71-0 

1019 

1113 

24-5 

207 

226 

48-0 

567 

619 

715 

1030 

1125 

25-0 

212 

233 

48-5 

576 

629 

72-0 

1041 

1137 

25-5 

220 

240 

490 

584 

638 

73-5 

1052 

1149 

260 

226 

247 

495 

593 

648 

730 

1063 

1161 

26-5 

233 

254 

50-0 

603 

658 

735 

1073 

1172 

270 

239 

261 

50-5 

612 

668 

74-0 

1084 

1184 

27-5 

245 

268 

51-0 

621 

678 

74-5 

1095 

1196 

28-0 

253 

276 

515 

630 

688 

750 

1106 

1208 

THE    I 


LATUM  Or   TW    DMCftAKGt   Of    WITH    TWBOCGB   0T««- 

The  practical  formula 

Uw  qua-  mm/m  in  a* 

■ 

1)       w        II    ■    <  ..II    •  m  x  1000; 
Id  which  formula, 

\V,  tiic  width  of 
II.  Uie  drpth  •  ■ 

edge  to  the  level  of  (he  water  in  the  IN 
The  Mlu»ing  table  ia  calculated  by  weans  of  tills  formula,  it 
being  supposed, 

:.  Tliat  the   I  Rata  "•' 

•005  mM  front  ■■ 

•  column  of  thi 

Third,  That  ' 

M  \L  P        •  t  and  Leabroe 

I  the  term  m. : — 


TW  l»n».  I 


jn,    ,  iliis   case    nro    given    in    the 

i  tan  "f  tin-  labia.    Tie  j 

• 

-  virtually  of  the  MOM  wi.llh  as  tlie 

only  a  little,  if 

M   d'An- 

■  Bt,  in.  is  equal  to  -43 

on  the  n  iwUlbe  found  in  die 

loan  of  the  fa 

the  afcl  of  ti  ikolatloii  for  determin- 

ing the  •  I  '  "■*•»  by  u  overshot  outlet,  reduoM 

I  — 

V        ■  If  the  tritlth  "f  the  m.  mitrer,  hy  the  mtmhrr 

mn,  awl  oom  I    '/  'A' 

ou/Zrt  in  lAc  fral  nJumn,  when  the  outlet  i-  narrower  than  tlie  water- 
.    and  wlen  foe  Vital    -  HM  A*  •''""• 

And  by  DM  mimVr  in  the  ihirj  column  OOfTI  tptmduig  to  ffce  Mm* 

is  of  the  Mine  width  as  toe  outlet, 
•  than  thai  of  flu  lower 

■ 

•  -mine  the  vol 

:   hy  an  overshot  outlet,  the  width  of 

jhj  of  the  overflow  '99  m..  • 
ription. 
It  will  bi  mm  fr I  mm  of  the  table,  thai 

h  nn  outlet  of  n  metre  in  width,  and  of    -"- 

- 


a ith  tlie 

Remark. — I: 

a  mean 

/  the  qnantit] 

■  In  width,  and  of  a  depth  ■ 

In  th.  lad,  for  1  metre  in  width,  will 

U-  beta 

136. 

| 

And  in  the  ■ 
width,  b  1 143  and  I  18,  will  l>o 

about   I 

Win  rue.  1  |ii  K   3  —  438  lit) 

TO   DETERMINE    THE    WTOTB  1HOT   IUTI.ET. 

349.  When  the  role  ed  per  leeond  is 

known,  and  it  ia  wiahed  to  calculate  Ihe  width  to  be  given  to  an 
oTorahol  outlet,  t  the  deeired  discharge 

\\i:h  a  given  height  "t  water,  this  may  !*•  done  in  the  following 

- : — 

■i  height 
(this  nn:  •  •  for  a  wi.llh  of  I  metre), sad 

litres,  it  trill  gi\e  lh< 
icitlth  in  i 

I  I  What   width  must   be  given  to  nn   0 

quired  to  discharge  BOO  litree  per  eeoond,  with  a  depth  al 
■  ! ■:•■  of  '13m. .' 

In  the  s ii.l  column  of  the  table,  and  o]  wDI  l>o 

found  the  nun. 
W.  have,  then  — 

:    T2  =  8-33  m..  the  width  - 
S  /  What  width  must  be  given  to  an  open  stains, 

required  wd,  with  ■  depth 

.  m. .' 

find  that  180  litres  is  the  effectual  d 
■  ■  a  wi.lih  of  i  metre. 
Whence — 

.  th.-  width  sought 

to   Dl  iii  HOT     in!    i  !  i  i  ii  "i     rffl    "1  ti.et. 
'  i    iv   < K-.nr   where  we  are  limited  as  to  width.      It  is 

then  in vi  s..irv  to  ascertain  the  least  depth  necessary  to  effect  tlm 
required  discharge,  which  maj  1~-  done  by  means  of  the  following 

rule  : — 

/),,„;.  /  in  hir>  <  ]tt  anond,  If  th'  wUfk  m 

mi  Com  the  mmtbtr  in  the  meani  omowi  wMol  it  w 

the  MOM  ii'  iJitmnnl,  (he  number  in  the  firtl  column  UN IMUUwJuU/ 
'.',  or  very  nearly  to. 


BOOK  OF  INDUSTRIAL  DESIGN. 


115 


Example. — With  what  depth  of  outlet  will  a  discharge  of  350 
litres  per  second  be  effected,  the  width  being  limited  to  2  metres  1 

We  have 

350  -=-  2  =  175  litres. 

In  the  second  column  of  the  table  will  be  found  the  number  176, 
corresponding  to  a  height  of  '22  m.  in  the  first  column,  which  will 
therefore  be  the  required  height,  witliin  a  millimetre. 

351.  Observation. — When  it  is  not  possible  to  measure  the 
depth,  H,  with  exactness,  the  lesser  depth,  h,  must  be  taken  im- 
mediately over  the  lower  edge  of  the  outlet,  and  multiplied  by  1-178, 
so  as  to  obtain  the  actual  value  of  H,  corresponding  to  the  num- 


bers given  in-the  table,  according  as  the  outlet  is  narrower  than  the 
reservoir,  or  water-course,  or  equal  to  it  in  width. 

First  Example. — Determino  the  discharge  effected  through  an 
outlet,  4  metres  wide,  the  depth,  k,  immediately  above  the  lower 
edge  being  equal  to  '11  in.,  the  width  being  about  four-fifths  of 
that  of  the  reservoir. 

We  have  '11  m.  x  1-178  =  -13  m.,  for  the  assumed  height,  H, 
of  the  reservoir  level. 

Corresponding  to  this  height,  we  have,  in  the  second  column,  the 
quantity,  82  litres. 

Then  82  x  4  =  328  litres,  the  effective  discbarge  sought. 


TABLE  OF  THE  DISCHARGE  OF  WATER  THROUGH  PIPES. 


Diameters  of  the  Pipes. 

Mean 

velocity 

'10 

■15 

•20 

m. 

■25 

m. 

•30 

m. 

metres 

per 

Discharge 

Fall 

Discharge 

Fall 

Discharge 

Fall 

Discharge 

Fall 

Discharge 

Fall 

second. 

per  metre 

per  metre 

per  metre 

per  metre 

litres 

in  length 

litres 

in  length 

litres 

in  length 

litres 

in  length 

litres 

in  length 

per 

per 

per 

second. 

centimetres. 

second. 

centimetres. 

second. 

centimetres. 

second. 

centimetres. 

second. 

centimetres. 

o-io 

0-8 

0-02 

1-8 

001 

31 

o-oi 

4-9 

o-oi 

7-07 

o-oi 

0-15 

1-2 

0-04 

2-6 

0-03 

4-7 

0-02 

7-4 

0-02 

10-60 

o-o  1 

0-20 

1-6 

0-07 

3-5 

0-05 

6-3 

0-03 

9-8 

0-03 

1414 

0-02 

0-25 

2-0 

0-10 

4-4 

0-07 

7-8 

0-05 

12-3 

0-04 

17-67 

0.03 

0-30 

2-3 

0-15 

5-3 

o-io 

9-4 

0-07 

14-7 

0-06 

21-20 

0-05 

0-35 

2-7 

0-19 

61 

0-13 

110 

o-io 

17-2 

0-08 

21-74 

0-07 

0-40 

31 

0-25 

7-1 

0-17 

12-6 

0-12 

19-6 

o-io 

28-27 

0-08 

045 

3-5 

0-31 

8-0 

0-21 

141 

016 

22-0 

0-12 

31-81 

o-io 

0-50 

3-9 

0-38 

8-8 

0-25 

157 

0-19 

24-5 

015 

35-34 

0-13 

055 

4-3 

0-46 

9-7 

0-30 

17-3 

0-23 

27-0 

018 

38-88 

0-15 

0-60 

4-7 

0-54 

10-6 

0-36 

18-8 

0-27 

29-4 

0-22 

42-41 

0-18 

0-65 

51 

0-63 

1 1-5 

0-42 

20-4 

032 

31-9 

0-25 

45-95 

0-21 

0'70 

5-5 

0-73 

12-4 

0-49 

L'l'll 

036 

34-4 

0-29 

49-48 

0-24 

0-75 

5-9 

0-83 

13-2 

0-56 

23-6 

0-42 

36-8 

0-33 

53-01 

0-28 

0-80 

63 

0-95 

141 

0-63 

25-1 

0-47 

39-3 

0-38 

56-55 

0-31 

0-85 

6-7 

1-06 

15-0 

0-71 

26-7 

053 

41-7 

0-43 

60-08 

0-35 

0-90 

7-0 

119 

15-9 

0-79 

28-3 

0-59 

44-2 

0-48 

63-62 

0-40 

0-95 

75 

1-32 

16-8 

0-88 

29-8 

0-66 

46-6 

0-53 

67-15 

0-44 

1-00 

7-8 

1-46 

17-7 

0-97 

31*4  • 

0-73 

49-1 

0-58 

70-7 

0-49 

1-10 

8-6 

1-76 

19-4 

117 

345 

0-88 

54-0 

0-70 

77-7 

0-59 

1-20 

94 

2-09 

21-2 

1-39 

37-7 

1-04 

58-9 

0-83 

84-8 

0-69 

1-30 

10-2 

2-44 

23-0 

1-63 

40-8 

1-22 

63-8 

0-98 

91-9 

0-81 

1-40 

110 

2-82 

247 

1-88 

44-0 

1-41 

68-7 

1-13 

98-9 

0-94 

1-50 

118 

3-24 

26-5 

2-16 

47-1 

1-62 

73-6 

1-29 

1060 

108 

1-60 

12-6 

3-68 

28-3 

2-45 

50-3 

1-84 

78-5 

1-47 

1131 

1-22 

1-70 

133 

4-14 

306 

2-76 

53-4 

2-07 

83-4 

1-66 

120-2 

1-38 

1-80 

141 

4-64 

318 

309 

56-5 

2-32 

88-3 

1-85 

127-2 

1-55 

1-90 

149 

5-16 

33-6 

3-44 

59-7 

2-58 

93-3 

2-06 

134-3 

1-72 

2  00 

157 

5-71 

353 

3-80 

628 

2-85 

98-2 

2-28 

141-4 

1-90 

2-10 

164 

6-29 

37-1 

4-19 

660 

314 

1031 

2-51 

148-4 

2-10 

2-20 

17-2 

6-89 

389 

4-60 

691 

3-45 

108-0 

2-76 

155-5 

2-30 

2-30 

18-0 

7-53 

40-6 

5-02 

72-2 

3-76 

112-9 

301 

162-6    ' 

2-50 

2-40 

18-8 

819 

42-4 

5-46 

754 

4-09 

117-8 

3-28 

169-6 

2-73 

2-50 

196 

8-88 

44-2 

5-91 

78-5 

4-44 

122-7 

3-55 

176-7 

2-96 

260 

20-4 

9-60 

45-9 

6-40 

81-7 

480 

127-6 

3-83 

183-8 

3-20 

2-70 

212 

10-34 

47-7 

6-89 

84-8 

517 

132-5 

414 

190-8 

344 

280 

22-0 

1111 

494 

7-41 

88-0 

556 

1374 

4-45 

197-9 

3-70 

290 

22-8 

11-92 

si -a 

7-94 

911 

595 

142-3 

"  4-77 

205-0 

3-97 

300 

236 

12-74 

530 

8-50 

942 

637 

1473 

510 

212-1 

4-25 

.  ICAL   DRAUGHTS 


I  ExoavatV.— \\~  Hi  tli.    like  data,  «  I 
U»r  diM-har.t-,  supposing  lb.  ilh  and 

d. pa  »»  UM  reservoir  ' 

H     =    13  m.   f..r 

M  ill  tile  liiird 
column. 

..■*— 

67  x   4  =  348  litre*,  (he  actual  discharge. 

OCTLET   WITH   A   STOUT,   Or: 

I:  may  happen  that  a  iipiiut  or  duct,  slightly  ioi 

■   ■   -  more  oontraet- 
rd,  both  at  the  bottom  and  at  '  -  v.  ■  .ir.     Ineuch, 

eaae,  the  discharge  Li  aenaibly  dim-rent;  ami  to  determine  it,  it  it 
neeesasry  to  multiply  tin-  nun  nd  column  of  tin-  table 

when  the  hi  ■-  upwards;  by  -8,  when  the 

blight  is  -15  m.;  and  by  "ti,  when  the  height  is  only  -1  m. 

TOES    FOR    71  v    OF    WATER. 

353.  The  formula*  employed  in  calculating  the  proportion*  of  a 
conduit  I  .  indrieel  tubes, 


V  =  53  58 


/  dY 
\         i     -»■ 


..:..! 


D  =  S  V       " 

4 


In  wUohi 

■  lodty ; 
D,  the  rolnme  is 

d,  th>-  internal  diune  I  luit; 

i     ■  ■         ■  •  i nit,  Abided  by 

the  lcw-ls  at  either  extremity  ;  and 
I  the  conduit 
In  ordiT  to  abri.l_'.-  the  calculations,  we  five  a  table,  with  the 
aid  of  which,  stive  to  the  laying  down  of 

water-ducta,  formed   by  cylindrical  tubes,  may  be  solved  very 
speedily. 

/  Example, — What  fall   must  Is-  given  to  a  conduit,    1  in.  in 

diameter!  in  ur.lcr  that  it   may  diacharge  n  litre.-,  of  water  pet 
nmond  ? 

From  tin-  table  it  will  Ik>  Been,  that  the  fall,  in  this  case,  should 
l»-    1  i-.,  or  1  millimetre.  |mt  i 

Second  Example. — What  diameter  must  be  Lri \  •  ■  1 1  to  a  conduit, 
600  metres  in  length,  in  order  thai  it  may  discharge  168 cobi 
of  water  i*-r  hour,  the  whole  Ball  being  460  m.1 

We  hare  168  onbic  metres.  ,,r  168,000  litres,  -=-  (60  x  60)  = 
46-65  litres,  discharged  per  leoond; 
and  :  '63c,  the  mil  per  o 

It  will  be  seen  from  the  table,  thai  the  dia ter 

this  discharge,  and  with  this  (all,  [a  ■•_'.')  in.,  or  SS  eentimi  I 


CHAPTER   Vin. 
AMPLICATION    OF  SHADOWS  TO   TOOTHED   GEAR. 


I'l.ATK    XXX. 


I    -      I       \  v  I.      J  . 


...  . 

in  a  fin  to  lav  down  tl at. 

;.  happen  to  be 

pply  the  finishing  ihadea  to  the  tpnr- 

■■  lv,  on 

each  wheel,  both  the  shadow  proper  of  tin-  external  rarmoe  of  tin- 

"f  the  tilth  apon  it,  end  als.,  upon  them- 

I  fat  with  one  of  the  wbeela  are  in.li- 

•  wheal, 

■01   In. 

to  lie-  luminous  pay, 

-.  by  the  radl  |     .  maring 

I  projection,  wi 

Hon.    Similarly,  by  tqnarlng 
bl  line,  i   ...  for  th< 

separation    of    light    and    atuule  on   tin-  outer  end.  of   tl 


Which  are  likewise  cylindrical.      A  portion  of  the  lateral  m. 

the  tec  tb  is  also  in  the  shade,  aa  will  easily  Ih-  determined, by  draw* 
-  through  the  extreme  .  parallel  to  the 

luminous  rays.      Thus  the  surfac. ■>.  n  </,  /'  *,  and  r I.  do  Ml 

any  light,  and  are.  therefore,  shaded  in  the  elevation,  as  within  the 

outlines,  a'  if  g  ft,  b'  e   ij,  and  <■'/'  k  I. 

shadow  ii|Kin  the  cylindrical 
'     .  »'/,  r'  I.  an 

their  shadows  on  the  web  are  also  vertical,    These  last  an 
mined  bj  drawing  the  laminar  lines  through  I  '. .-.  and 

«',  />',  i-',  and  thi  -  of  contact,  at,  n, ...  t.. 

ru',  ;i',  '/. 

To  complete  the  thadovi  i  of  the  t-  eth  upon  the  web,  it  is  farther 

)  t.i  obtain  the  outline  correeponding  to  the  edges,  a  d,  l<  a, 

extreme  points, ./,»'./.  and  »»'.  n,  <>'. 

and  in  n  Where,  however,  greater 

•  quired,  it  i«  well  to  find  ■  few  intermedial. 
The  lower  edge  of  the  tooth,  shadow  upon  the  web, 

which  is  obtained  in  U  er,  by  drawing  laminar  Bnea 

throuoh  tin-  points.  ;.../.  r.  tn.  •  .  .   ofthoweb 


BOOK  OF   INDUSTRIAL  DESIGN. 


Some  of  the  teeth,  also,  cast  shadows  upon  each  other ;  but  as 
their  surfaces  are  vertical,  these  shadows  are  simply  determined  by 
the  contact  of  the  luminal  lines  with  them.  Thus,  the  edges  pro- 
jected in  s,  I,  y,  &c,  have  for  shadows  the  straight  lines  projected 
vertically  in  u'  u',  x'  x',  z'  z3. 

Finally,  when  we  have  drawn  the  horizontal  projection  of  the 
wheel,  as  in  the  present  example,  we  have  to  determine  the  shadow 
east  by  the  web  upon  the  tenons  of  the  teeth,  and  upon  the  arms, 
or  spokes.  All  these  surfaces  being  horizontal  and  parallel,  the 
shadow  cast  upon  each  will  be  a  circle  equal  to  the  one,  hil, 
which  is  the  projection  of  the  inner  edge  of  the  web.  All  that  is 
necessary,  then,  is  to  draw  through  the  centre,  o,  o',  a  line  parallel 
to  the  luminous  ray;  and  to  find  the  points  of  intersection,  o3  and 
o3,  with  the  planes,  iw  o"  and  N  o"',  in  which  lie  the  upper  surfaces 
of  the  tenons  and  of  the  arms,  and  to  describe  arcs  with  the  points, 
o3  and  os,  as  centres,  and  with  the  common  radius,  o  h  (280).  In 
the  same  manner  we  obtain  the  shadows  cast  by  the  boss  of  the 
wh.el,  and  by  the  feathers  upon  the  arms. 

When  we  have  thus  gone  through  the  requisite  operations  for 
eaeh  wheel,  we  proceed  with  the  shading,  according  to  the  prin- 
ciples laid  down  (289,  et  seq.),  covering  first  the  portions  which 
require  a  more  pronounced  shade,  and  leaving  the  lighter  parts  to 
the  last. 

The  specimen,  fig.  A,  which  we  recommend  to  be  copied  on  a 
arger  scale,  indicates  the  various  gradations  of  shade  required  to 
produce  the  proper  effect,  according  to  the  different  positions  of  the 
planes,  and  to  the  contour  of  the  surfaces.  These  wheels  are  also 
supposed  to  be  mounted  upon  their  shafts,  which  are  shaded  as 
polished  cylinders. 

bevil    wheels. 
Figures  3  axd  4. 

355.  The  procedure  here  called  for  will  be  the  same  as  in  the 
preceding  case— that  is  to  say,  we  must  first  draw  the  outlines  of 
the  shadows,  proper  and  cast,  for  each  wheel.  The  figures  repre- 
sent a  horizontal  and  vertical  projection  of  a  bevil  wheel  with  east- 
iron  teeth,  the  shadows  being  indicated  on  the  different  surfaces. 

The  external  surfaces  of  the  teeth  and  of  the  web  being  conical, 
the  shadows  proper  are  determined  in  the  same  manner  as  for  the 
cone,  by  drawing  through  the  apex  a  plane  parallel  to  the  luminous 
ray,  and  finding  the  generatrix  at  which  this  plane  touches  the 
conical  surface  (313). 

It  is  in  this  manner  that,  for  the  outer  ends  of  the  teeth,  we  ob- 
tain the  generatrix  projected  in  o  a,  fig.  3,  and  for  the  outer  surface 
of  the  web.  that  projected  in  o  B.  These  generatrices,  which  are  the 
lines  of  separation  of  light  and  shade,  are  projected  vertically  in  tho 
straight  lines,  o'  a'  and  d'  b',  converging  to  the  apex  of  the  cone; 
since,  however,  these  lines  occur  between  two  teeth  in  the  present 
example,  they  are  not  apparent  in  fig.  4. 

Some  of  the  teeth  have  their  lateral  faces  in  the  shade,  whilst  all 
the  lower  conical  surface  corresponding  to  the  wider  ends  of  the 
teeth  is  in  deep  shade,  as  indicated  in  fig.  4  by  a  darker  tint. 

We  have,  besides,  merely  to  determine  the  shadows  cast  by 
the  outer  edges,  a  d,  b  e,  cf,  and  by  the  curved  portions,  d  g,  e  h, 
and  f  i.  Now,  the  outer  edges,  a  d,  b  e,  cf,  cast  shadows  upon 
the  conical  surface  of  the  web,  which  are  represented  by  straight 


lines  coinciding  with  generatrices  on  this  surface ;  and  therefore, 
to  determine  them,  we  must  draw  through  the  corresponding  edges 
a  series  of  planes  parallel  to  the  luminous  ray  ;  the  whole  of  these 
necessarily  passing  through  the  common  apex,  o,  it  is  simply  re- 
quisite, therefore,  to  find  the  shadow  east  by  any  ono  point  in 
these  edges.  Let  us  take,  for  example,  the  points,  d,  e,  /.  all 
situate  in  the  same  circle,  E  d  F ;  the  operation,  then,  is  to  find 
the  shadow  of  this  circle  upon  the  conical  surface,  and  is  the  same 
as  that  which  we  have  already  indicated  and  explained  several 
times ;  it  consists,  in  fact,  in  drawing  any  planes,  G  h  and  I  J,  per- 
pendicular to  the  cone's  axis,  and,  consequently,  parallel  to  the  plane 
of  the  circle,  e  d  f. 

356.  We  have  seen  that  the  shadow  cast  by  the  circle,  e  d  f, 
upon  each  of  the  planes,  will  be  a  circle  equal  to  itself;  and  it  is, 
therefore,  simply  necessary  to  find  the  shadow  cast  by  the  centre, 
o,  o'.  This  shadow  falls  in  o,  o',  on  the  plane,  G  H,  and  in  o3,  o3,  on 
the  plane,  I  I ;  if,  then,  with  the  points,  o  and  &3,  as  centres,  and 
with  the  radii,  o  k'  and  o*  ]',  equal  to  the  radius,  o  E,  we  draw  a 
couple  of  arcs,  these  arcs  will  cut  the  circles,  g'  k'  h'  and  I'  l'  j',  <h ) 
projections  of  the  sectional  planes,  in  the  points,  k'  and  j',  wlrvl ., 
being  squared  over  to  the  vertical  projection  in  the  points,  K  and  <, 
will  give  two  points  in  the  curve,  J  K  M  N,  representing  the  shado  v 
cast  by  the  circle,  E  d  f,  upon  the  conical  surface  of  tho  wej. 
Consequently,  if  we  draw  the  luminar  lines  through  the  points, 
d\  e',f,  &c,  the  respective  points  of  their  intersection  with  the 
curve,  as  M,  p,  Q,  will  represent  their  shadows  cast  upon  the  web 
surface..  These  points  are  squared  over  to  m',  p',  q',  in  the  h  >ri- 
zontal  projection. 

The  points,  g,  h,  i,  situated  upon  the  upper  base  of  the  cone, 
obviously  cast  no  shadows,  the  shadows  of  the  teeth,  however, 
springing  from  them ;  if  it  is  wished  to  determine  any  points  be- 
tween these  and  those  already  found,  it  will  be  necessary  to  de- 
scribe an  imaginary  circle,  such  as  g',  k',  h',  passing  between  the 
points,  d  and  g,  the  cuter  and  inner  angles  of  the  teeth.  Tho 
curve,  r  s  T,  as  projected  in  the  elevation,  will  be  found  to  repre- 
sent the  shadow  cast  by  this  circle  upon  the  conical  surface  of  tho 
web. 

As  the  edges,  ad,be,cf,  cast  shadows  which  coincide  with 
generatrices  of  the  cone,  they  may  be  obtained  simply  by  drawing 
straight  lines  through  the  several  points,  m\  q',  and  p',  converging 
in  the  apex  of  the  cone  in  both  planes  of  projection. 

Finally,  the  shadows  cast  by  some  of  the  outer  edges  of  the 
teeth,  such  as/c,  upon  the  teeth  immediately  behind,  are  defined 
by  drawing  the  luminar  line,//,  through  the  point,/,  meeting  the 
flank,  /  m,  of  the  other  tooth,  which  lies  in  a  vertical  plane.  This 
point  of  contact  is  projected  vertically  in  V,  on  the  vertical  projec- 
tion,/ f,  of  the  luminar  line.  It  now  remains  to  draw  a  line,  I'  n, 
through  this  point,  V,  and  through  the  apex  of  the  cone,  and  this 
line  will  represent  the  shadow  cast  by  the  edge,/c. 

357.  In  the  case  where  the  luminar  line  passing  through  the 
extremity  of  the  tooth— as  that,  for  example,  drawn  through  the 
point,  p — falls  upon  a  curved  portion  of  the  tooth  behind,  it  is 
necessary,  if  great  accuracy  is  required,  to  imagine  a  vertical 
plane  passing  through  this  point  and  through  the  luminar  line, 
and  then  to  find  the  intersection  of  this  plane  with  the  curved  sur- 
face of  the  tooth.     This  would  require  a  separate  diagram;  but 


THE    I  «IAVH 


-unpfe,  0£.  B   ' 

It  ■•'.  ili»t 

■ 

Id  sb 

■  :.  that,  from   I 

- 
in  uV  »luul.-,  ■  I   end  of  the  other  i»  illumi- 

nalt-d. 


APPUCATiON  OF  SHADOWS  TO  SCREWS 
PLAT!    XXXI. 

by  at' 

■ 
.1   i«th.      TK-  ntly,  called   bri 

1 
cast  »h*J'>»«  u|hiii  tin-  .-..rv  ■•!   tbe  KNW,  nr  opon  the  twisti 

I  Itself.  If  the 
anew  in  surmounted  by  n  head,  there  will  !»•,  in  addition,  the 
►ha.1..  •  •  of  the  thread 

"a,  U|«  v.  i  to  explain  the  methodi 

esrewe. 

Tim  limit  of  the  ehadow  proper  np  in  tbe  screw,  i- 

-  tlmt  iijH.n  a  right  cylinder,  by  drawing  the 

nuliui,  o  a,  »t  right  engtea  t"  the  ray  "f  light,  r  ".  and  then  squar- 

:  lint,  a,  to  a'  and  a*,  and  drawing  aline  through  theae 

1 1 1 1 ••  -  mum  manner  we  obtain, 

the  i-'int,  n,  tbi  light  and  shade, 

1'  B*.  u|»in  tl 

'n„.  the  Ibreadi  ir[...n  the 

:i|i!v  determined  l.y  n 
D  i/,  drawn  parallel  t"  tbe  Ini 
i  ./  n.  the  projection  of  (be  core,  in  t  and  •/: 

ti,r-  I.-,".  /',  paralli  I  t"  I 

■  • 

■  r\.  i|  outline  of  the  -■ 

i  to  the  left,  :i 
8*  en<l  I  and  'J, 

ihadowa 

■ 


1 1..  be  tbe  tun 

■   ' 

■  ■f  tlir  I 

in  both  •  ' 

which  \*  borixi 

I  .  I.  i  a  ii  i.  whicl 

from  the  left-banded  portioa  i  upon  a 

which  will  lx-  i 
termined,  in  aecordanci'  \\th  j 
tbe  principal  polnta  in  which  13. 


J     AM'    5. 


861.  Tin'  construction  of  the  shadows  of  a  roctangular-l 
•  the  same,  win  ther  it  bo  in  a  horizontal  i>r  \. 
or  whether  it  Ii'  right-handed  nr  left-handed.    Tim-,  tl.. 
with  eevi  I  and  A,  has 

in  tin-  Brat  puce  a  shadow  proper,  limited  by  tbe  vertical  line,  a'  a', 

i  r  from  tbe  point,  a,  and  next,  the  shadow, 
cast  upon  the  core  bj  lb<  out*  i  i dge  of  tbe  dm  ad,  i '  d*  i.'  ;  tl»  re 
over,  :i  |N.rti.m  of  tin'  shadow  cast  by  the  circular  shoulder, 
i.  ii  i,  upon  the  Ihreada,  inn!  also  upon  the  core.    Tin-  onl 
.  idowa  are  fonnd  in  | 
.   and  3  (361). 

1i:i  urot  LAI  •   uw. 

Fun  sal  t,  i'.',  7,  am.  s. 

\: 

■    of  which  the  height,  a  A,  ia  greater  than  tbi 
the  base,  e  </.  there  "ill  be  a  shadow  cast  by  the  outer  edgi 
thread  upon  tbe  twisted  surface  oft]  involution.    In 

proceeding  to  determine  tl ntline  of  t } i i -.  shadow, 

with  the  genera]  method,  which  eonaiata  in  finding  die  i 
eontael  of  the  luminous  rays  with  tbe  surface,  we  are  I"! 
in  the  lir-t  place,  the  curre  of  intersection  ol  a,  with  n 

plain-  passing  through  tin'  luminous  ray,  and  parallel  t"  tl" 

tip-  screw. 

i  purpose,  lot  ■  o,ftg.  1  ;  Ma  lo- 
in with  tli I  Mhti  ad  will  I*. 

in  the  i                        8  and  7.  and  similarly  it>  intersection  with 

tlir  inside,  n  1 g,  will  lx'  in  tbe  point,  r,r.  To  obtain  mtertne- 
■  onal  curve,  we  i 

with  tl"  I  r.-lilii.  o  m,  o 

.  indora,  on  which  UetheheUi  between 

the  inner  one,  «  /  g,  nm'  outermost,  •/ 1 '  ■>.  I 

•  !.  r     \\ .  tin  reb]  obtain  lion,  A.  i, 

i  ..\.  r  to  h .  r.  in  fig.  ii.  and  men,  by 

of  Inter- 

■ 

i  aw  »  luminal  Una,  ».'  •  '.  through  tin-  point,  i '.  in  the  mum 


BOOK   OF    INDUSTRIAL   DESIGN. 


plane,  its  intersection  with  the  curve,  e"  h'  i'  r,  will  give  a  point,  e', 
in  the  outline  of  the  shadow  sought. 

In  like  manner,  by  drawing  other  planes,  as  f  h  and  g  r,  parallel 
to  the  Hist,  e  o,  wo  shall  obtain  (he  intersection*!  curves,  f2/'  h' 
and  o2/  g  I,  and  further  upon  these  the  points,/'  and  g',  of  the 
outline  of  the  shadow.  By  proceeding  thus,  we  can  obtain  as  many 
points  as  may  be  deemed  necessary  for  the  construction  of  the 
shadow  cast  by  the  outer  edge,  c  g'  p,  of  the  thread,  and  the  curve 
obtained  is,  of  course,  repeated  on  the  several  convolutions  of  the 
thread.  We  would  remark,  that  there  is  no  shadow  cast  when  the 
depth  of  the  thread  is  such,  only  that  a  b,  fig.  6,  is  less  than  the  half 
of  the  base,  c  d,  of  the  generating  triangle. 

The  diagrams,  figs.  6"  and  8,  which  represent  a  portion  of  a  left- 
handed  screw,  will  show  that  the  operations  required  in  this  modi- 
fication, to  determine  the  outlines  of  the  shadows,  are  precisely  the 
same  as  those  last  explained. 

The  core,  N,  which  separates  the  two  portions  of  the  double 
screw,  as  well  as  the  end,  n',  receives  a  shadow  cast  by  the  outer 
edge  of  the  adjacent  convolution  of  the  thread. 

shadows  upon  a  round-threaded  screw. 
Figures  9  and  10. 

363.  These  figures  represent  a  species  of  screw  generated  by  a 
circle,  abed,  the  plane  of  which  passes  through  the  screw's  axis, 
and  of  which  each  point  describes  a  helix  about  the  same  axis. 
The  intervals  or  hollows  between  the  convolutions  of  the  thread 
are  also  formed  with  a  helical  surface  generated  by  a  semicircle, 
d  e  f,  tangential  to  the  first.  We  have,  then,  to  determine  the 
limiting  line  of  the  shadow  proper  upon  the  screw,  and  the  shadow 
cast  by  this  line  upon  the  hollows. 

The  projecting  thread  being  a  species  of  spiral  torus  or  serpen- 
tine, the  determination  of  its  shadow  will  be  similar  to  that  of  the 
shadow  of  the  ring  (323). 

Thus,  if  the  screw  be  sectioned  by  a  vertical  plane,  G  o,  passing 
through  its  axis,  iU  intersection  with  the  thread  will  evidently  be  a 
circle,  as  projected  in/  I',  fig.  9.  This  circle,  being  inclined  to  the 
vertical  plane  of  projection,  fig.  10,  is  projected  therein  in  the  form 
of  an  ellipse,  the  principal  points,/  k,  I,  of  which  are  obtained  by 
squaring  over  the  points,/,  k\  V,  respectively,  upon  the  helices  cor- 
responding to  the  points,  a,  b,  c.  If,  then,  upon  the  plane,  G  o, 
which  we  suppose  to  be  reproduced  at  o  g,  fig.  10*,  we  project  the 
luminous  ray,  R  o,  it  will  be  sufficient  to  determine  the  point  of 
contact  of  this  ray  with  the  curve,,;'  A:  I;  for  this  purpose,  find  tho 
projection  of  the  ray  upon  the  vertical  plane  in  g'  o',  fig.  10";  then 
draw  a  line,  g3  <?,  tangential  to  the  ellipse,  j  k  I,  and  parallel  to  the 
straight  line,  g1  o,  its  point  of  contact,  m,  with  the  ellipse  will  be  a 
point  in  the  line  of  separation  of  light  and  shade  upon  the  outer 
surface  of  the  screw-thread.  By  proceeding  in  this  manner,  any 
number  of  points  in  this  line  may  be  obtained. 

By  continuing  the  sectional  plane,  G  o,  across  the  hollow  of  the 
screw,  we  shall  likewise  obtain  the  elliptic  curve,  n  o",  the  principal 
points  in  which  are.  equally  situated  upon  the  helices  which  pass 
through  the  points,  d,  e,/;  it  is  sufficient  to  prolong  the  luminar 
line,  g1  o3,  until  it  cuts  the  ellipse,  n  o'  p,  so  as  to  obtain  the  point, 
<A  which  is  the  shallow  cast  by  the  corresponding  point,  m,  of  the 


line  of  separation  of  light  and  shade  upon  the  hollows  or  intervals 
between  the  convolutions  of  the  thread. 

It  is  to  he  remarked,  that  the  prolongation  of  the  line  of  separa- 
tion of  light  and  shade,  s  I,  casts  a  shadow  upon  the  outer  surface 
of  the  convolution  immediately  below;  and,  in  the  same  manner, 
the  shoulder  above  casts  a  shadow  over  the  projection  and  hollow 
of  thr  adjacent  thread. 


APPLICATION  OF  SHADOWS  TO  A  BOILER  AND  ITS 
FURNACE. 

PLATE    XXXII. 

shadow  of  the  sphere. 

Figure  1. 

364.  It  will  be  recollected,  that  a  sphere  is  a  regular  solid,  gene- 
rated by  the  revolution  of  a  semicircle  about  its  diameter.  From 
this  definition  it  follows,  that  its  convex  or  concave  surface,  ac- 
cording as  it  is  considered  solid  or  hollow,  is  a  surface  of  revolution, 
of  which  every  point  is  equally  distant  from  the  centre  of  the  gene- 
rating circle.  To  determine,  then,  the  shadow  proper,  upon  the 
surface  of  a  sphere,  we  can  proceed  according  to  the  general  prin- 
ciple (328)  ;  but,  in  this  particular  case,  the  following  will  be  the 
simpler  method. 

Let  us  suppose  the  sphere  to  be  enveloped  in  a  right  cylinder, 
having  its  axis  parallel  to  the  luminous  ray  ;  this  cylinder  will  touch 
the  sphere  at  a  great  circle,  which  is,  in  fact,  the  line  of  separation 
of  light  and  shade,  and  the  plane  of  which  is  perpendicular  to  tho 
luminous  ray,  and,  consequently,  inclined  to  the  planes  of  projec- 
tion ;  it  follows,  therefore,  that  the  projection  of  this  line  upon  those 
planes  will  be  an  ellipse. 

Thus,  let  fig.  1  represent  the  horizontal  projection  of  a  sphere, 
whose  radius  is  o  a,  the  projections  of  the  extreme  generatrices,  B  c 
and  D  E,  of  the  cylinder,  parallel  to  the  luminous  ray,  touch  the 
external  contour  of  the  sphere  in  the  points,  c,  E,  which  are  dia- 
metrically opposite  to  each  other,  and  are  the  extremities  of  the 
transverse  axis  of  the  ellipse. 

As,  in  general,  this  curve  can  be  drawn  when  its  two  axes  are 
determined,  it  merely  remains  to  find  the  length  of  its  conjugate 
axis.  To  this  effect  let  us  imagine  a  vertical  plane  to  pass  through 
the  luminous  ray,  R  0,  and  let  us  take  two  lines  tangent  to  the 
section  of  the  sphere  in  this  plane,  and  parallel  to  the  luminous 
ray ;  if  now  we  turn  this  plane  about  the  line,  R  o,  considered  as 
an  axis,  so  as  to  fold  it  over  upon,  and  make  it  coincide  with,  the 
horizontal  plane,  the  great  circle,  which  is  its  section  with  tho 
sphere,  wall  obviously  coincide  with  the  circle  drawn  with  the 
radius,  a  o.  The  luminous  ray  will,  as  already  seen  (287),  be 
turned  over  to  r'  o,  making  an  angle  of  35°  16'  with  the  line,  R  o. 
It  may  also  be  obtained  by  making  the  line,  r'  r,  perpendicular  to 
r  o,  and  equal  to  a  side  of  the  square,  as  G  K,  and  then  joining 
r'  o.  The  two  luminous  rays  tangential  to  the  sphere  will  then 
coincide  with  the  straight  lines,  H  L  and  M  N,  parallel  to  r' o, 
their  points  of  contact  with  the  great  circle  will  be  the  extremities 
of  the  diameter,  L  N,  perpendicular  to  r'  o.  If  now  we  imagine 
the  plane  to  be  returned  to  its  original  position,  the  points,  l  and 


TIIK    I 


*.»;::  br  pr..j,<-i«-d  in  l' at-:  ng  the  length 

tin-  conjugal*  utt  of  the  elbpae  aought. 

364.  If,  in  place  ••:  ■  rdinary 

■ 
a  arrira  of  an- 

'  ■ 

B  Ot  end 
luriursl    In    :..-•   plane,  so  that  it  shall  coincide  uilli   tin-   I. 

with  the 
".  of  the  »)•: 

the  radius,  e  o,  equal  to  a  c.     Next  draw  the  tan- 
»'  u,  and  then  project  the  point,  i,  on  tlie 
thamcU-r,  I.    a,  '  original  line  of  section,  ami 

-  manner,  as  many  points  ma;. 
lained  .1-  lO  cef,<f 

.  now  apparent 
part  of  the  ellipse. 

If  tl:.  poaed  l"  1"-  upon  the 

r..  would,  on 

arr,  be  in  the  direction,  a  t,  jieriK'nilicular  ; 
fig.  3,  representing  the  Itenilenhwrical  end  of  a  boiler,  shaded  and 


siui"  L  BOIXOW  n  HERB. 

- 

866.  When  i  by*  plane  passing  through  ita 

centre,  and  parallel  to  the  plane  of  projection,  the  inner  edge  of  the 
aviD  east  a  shadow  u|H,n  tin-  concave  «*",  the  outline 
■  will  U-  an  elliptic  curve,  which  may  be  determini 

:•  ral    principle   of   pa  already 

■  of  the  simpler  I  'lis  and 

auiiliar;.  nple,  md  of  which  wu 

ahall  pi  another  inatai ,  in  li::.  2. 

re  np.n 

■   - •  -«■  ti» •  ri  throogfa  the  line.  1 — 3, 

of  the  boiler,  i  '.  and  6.     It'  this  bemisphera  be 

••,  a  b,  parallel  to  the  lominoni  r«y, 

■   ;  in  the  auxiliary  view,  fig.  3,  will  b< 

-  ray,  lying  in  this  plane,  and  passing 
;  >int,  a,  a',  will,  in  fig.  8,  Is-  repn  seated  by  tin-  line, 

-  indicated   in    | 
I  ill    line,  a'  i  ',  • 

■  ',  Which  muit   l>e  - 

d  o  will  !»•  tic  •  by  tlio 

point,  A. 

In  the  earne  >  tela  the  pointa,  >'. ,/,  bj  m  ua  of  the 

a  n,  and  catting  the  sphere  in 

I 

■i'  li',  parallel   I 

■ 

0M  tra: 

ml  aii,|  mechanical  subject* ;  as,  for  i 
n  niches,  domes,  and  boilers. 


arrucATioss. 

sal  section,  at  the  line,  3 — I, 

ends,  ai  I  f  cylindrical  ch 

-  ..  . 

ii   ii)«.ii  it,  ami 

.•■n,  made  at  the  line,  5 — 6,  in  fig*.  4 
and  5. 
Fur  thin  boUer,  we  have  to  deteramu — 

I  |"'n  the 

andj  k  A  upon  the  cyliodrical  surface,  together  with  tlie  ■ 
cast  on  the  i'    •  ndrieal  chan. 

•  rnal  cylindrical 

and  spherical  porb'ona  of  the  boOer,  and  Ih  -;  uj».n 

.  the  cylindrical  chambara, 

1  letter*  as  to  the  analogous  diagram, 

fig,  3,  this  view  being  drawn  for  the  pn  >ing  the  elliptic 

carve,  n  J  c,  of  the  shadow  east  by  the  ciivular  portion,  a  c  d,  up»n 

the  internal  spherical  surface  <>f  tlie  end  of  the  boiler. 

In  the  same  manner  ia  obtained  the  portion,  e  h  c  1,  by  means of 

the  diagram, fig.  8,  observing  that  the  sections  made  parallel  to  (lis 

rav  of  light!  above  the  line,  " 

below,  Mieli  aa  y  c,  give  the  circular  portion  to  the  righl  of  the 
.  but  an  elliptical  portion  to  the  left  of  t!,  - 

the  cylindrical  port  of 
the  boiler  obliquely.  It  must  U-  remarked,  that  the  ejrlindrieal 
chambera,  sttnatea  on  tne  top  of  the  boiler,  give  rise  to  the  niter. 

i,  i  j  E  r,  which  i  i  upon  the  interior  of  tin 

instead  of  the  rectilinear  portion,  i  r,  of  the  i  -atrix  .  >f 

the  cylinder,  which  would  have  cast  a  shadow,  bad   the  cj 

chambers  not  been  ' 

-i  ladoVI   east  bj 

limited  to  the  curves,  jki,  which  may  be  • 
the  aid  i  ■    by  squaring  over  0m  i 

to  the  are.  j'  k'  l'  I ',  and  then  drawing  a  aerial  of  lamia 
through  that  i«,  lines  parallel  to  tin 

These  will  meet  the  internal  surface  of  the  cylinder  in  lb 
j',  A',  /',  which  an-  squared  over  again  t"  the  longitudinal  - 
fig.  I,  b\  nu  ans  i.t  horizontals 

through  the  com  ■ponding  points  in  I        "  ■■  h  chamber,  in 

tin-  points,  j,  /..  I.    The  rectilinear  portion,  t  i,  of  tin-  nppermosl 
\  of  the  cylinder,  lias  for  Its  shadow,  on  the  internal  sur- 
[Ual  straiglit  line.  /  i.  which  e> 
in  the  projection,  with  the  axis,  o  0 

neratrix,  I  *,  of  each  cylindri- 
cal chamber,  li!  -h.ul.iw   upon   tlie   internal   Burl 

tin-  boUer,  tl atlin*  of  which  h  ■  ourve,  i  mjt  wb 

•      !re,  ii.  and  Wtthj 

equal  to  that,  c  <>,  ••(  the  boQer.    11 

lit  line    i  n.  which  i     -  i.dieulnr  to  ti- 

the cylinder;  whilst  :; 
■'.mi. 
\\  .    .  :     .  .    ■:..    points,  i,  m,j,  of  tlie  enrxe, 


BOOK  OF  INDUSTRIAL  DESIGN. 


independently,  with  the  assistance  of  the  auxiliary  projection,  fig.  6, 
at  right  angles  to  fig.  4. 

It  is  the  same  with  the  curve,  n  p  q,  which  is  likewise  an  arc.  of 
a  circle,  because  the  straight  line,  n  p,  the  edge  of  the  cover  which 
closes  the  top  of  the  chamber,  is  at  right  angles  to  the  axis  of  the 
latter,  and  at  the  same  time  parallel  to  the  vertical  plane  of  projec- 
tion. The  edges,  n  r  and  r  m,  being  vertical,  have  for  shadows 
upon  the  internal  surface  of  the  chamber,  a  couple  of  vertical 
straight  lines,  parallel  to  themselves  (309).  The  chamber  to  the 
right  having  a  circular  opening  in  the  cover,  has  a  shadow  upon  its 
internal  surface,  necessarily  different  from  that  in  the  other  cham- 
ber. It  is,  however,  easily  obtained,  and  in  the  same  manner  as  in 
figs.  1  and  1°,  Plate  XXVIII.  It  must  be  observed,  however,  that 
a  portion,  s  (  u,  of  this  shadow  is  due  to  the  under  edge,  s  T  u,  of 
the  cover-piece  :  whilst  the  other  part,  s  v,  takes  its  contour  from 
the  upper  edge,  v  x,  of  the  same  piece.  A  comparison  of  figs.  4 
and  5  will  render  these  points  ea§y  of  comprehension. 

There  remains,  finally,  the  curve,  c  e  g  h,  and  the  rectilinear  por- 
tion, h  i,  together  extending  from  the  first,  d  d  c,  to  the  straight 
line,  i  i,  and  which  represents  the  shadow  cast  by  the  arc,  A  F,  g  h, 
of  the  hemispherical  end  of  the  boiler,  and  the  straight  part,  H  I,  of 
the  upper  edge  of  the  cylindrical  portion. 

The  whole  curve,  D  d,  c  g  i,  representing  the  shadow  cast  by 
the  edge  of  the  section  of  the  boiler  upon  the  internal  surface  of 
the  latter,  is  precisely  the  same  as  that  distinguished  in  architecture 
by  the  name  of  the  niche  shadow.  It  is  to  be  observed,  however, 
that  the  position  in  this  case  is  different,  as  the  axis  of  the  niche  is 
vertical. 

We  have  now  to  draw  the  shadows,  proper  and  cast,  upon  the 
outer  surface  of  the  boiler,  as  seen  in  horizontal  projection,  fig.  5. 
As  for  the  shadow  proper,  it  consists  partly  in  that  limited  by  the 
line  of  separation  of  light  and  shade,  d  d,  obtained  by  the  tangential 
line,  making  an  angle  of  45°  with  the  horizon,  and  touching  the 
circle  in  the  point,  c,  and  partly  in  that  bounded  by  the  elliptic 
curves,  c  d  and  d  c'  E,  upon  the  spherical  ends  of  the  boiler,  the' 
manner  of  determining  which  has  already  been  thoroughly  discussed 
in  reference  to  fig.  1. 

.  368.  As  to  the  shadows  cast  by  the  cylindrical  chambers,  either 
oil  their  neck  pieces,  or  upon  the  outside  of  the  boiler  itself,  they 
are  simply  represented  by  lines  inclined  at  an  angle  of  45°,  as  a'  d', 
B'gE',  drawn  tangential  to  the  outsides  of  the  cylinders,  and  which 
are  prolonged  in  straight  lines,  as  far  as  the  line  of  separation  of 
light  and  shade,  upon  the  cylindrical  portion  of  the  boiler;  that  is, 
in  case  they  stand  out  far  enough  from  the  boiler  surface.  If,  on 
the  contrary,  they  do  not  rise  very  high,  as  exemplified  in  the 
end  view,  fig.  9,  it  will  be  necessary  to  determine  the  outline  of 
the  shadow  cast  by  a  portion  of  the  upper  edge,  b'  c',  as  lyino- 
either  upon  the  cylindrical  part  of  the  boiler,  or  upon  one  of  the 
spherical  ends.  To  find  the  shadow  in  this  last  case,  we  have 
supposed  an  imaginary  vertical  plane  to  pass  through  the  luminous 
ray,  r'  o',^fig.  5,  producing  an  elliptical  section  of  the  cylinder, 
and  a  circular  one  of  the  spherical  part.  This  plan  being  repro- 
duced at  r3  o",  fig.  9,  and  turned  about,  to  coincide  with  the  hori- 
zontal plane,  we  have  the  curve,  F3  Ga  h2  ,  representing  the  section 
in  question.  The  point  of  contact,  b',  being  transferred  to  b2,  is 
also  turned  down,  as  it  were,  upon  the  horizontal  plane,  to  the 


point,  B3;  so  that  if  we  draw  a  line,  Es  I*,  through  this  point,  B* 
parallel  to  the  luminous  ray,  r3  o3,  similarly  brought  into  the  hori- 
zontal plane,  this  line,  b3  i2,  will  cut  the  intersectional  curve  in  the 
point,  Is ;  the  horizontal  projection,  I3,  of  this  point,  upon  the  line, 
R3  h2,  being  obtained  by  letting  fall  the  perpendicular,  I3  i3,  upon 
the  latter.  The  corresponding  point,  i',  in  fig.  5,  is  taken  at  a  dis- 
tance from  b',  equal  to  b2  i3,  in  fig.  9.  Proceed  in  the  same  manner 
with  another  sectional  plane,  parallel  to  the  first,  and  passing 
through  the  point,  o',  in  order  to  obtain"  a  second  point,  c',  of  the 
shadow.  The  operations  necessary  for  determining  the  intersec- 
tional curves  are  sufficiently  indicated  in  figs.  5  and  9. 

369.  The  cylindrical  steam-boiler,  represented  in  longitudinal 
section  in  fig.  A,  in  end  elevation  in  fig.  g},  and  in  transverse 
section  in  fig.  ©,  conjoins  the  various  applications  of  shadows,  of 
which  we  have  been  treating,  in  reference  to  spheres  and  cylin- 
ders ;  whilst,  at  the  same  time,  they  serve  as  examples  of  shading, 
by  lines  or  by  washes,  indicating  the  effects  to  be  aimed  at,  and  to 
be  attained  by  the  following  out  of  the  various  principles  already 
laid  down. 

370.  We  must  remind  the  student,  that,  in  order  to  produce  tnese 
effects,  he  'must  not  always  confine  himself  to  the  representation 
of  the  shadows  proper  and  cast  merely.  lie  must,  further,  show 
the  gradations  of  the  light  or  shadow  upon  each  part,  as  has  already 
been  explained  with  reference  to  solid  and  hollow  cylinders.  As 
upon  a  cylinder  or  a  cone,  there  is  always  a  line  of  pre-eminent 
brilliancy,  so  likewise,  upon  the  surface  of  a  sphere,  will  there  be  a 
point  of  greater  brilliancy  than  the  rest. 

This  point  is  actually  situated  upon  the  luminous  ray,  passing 
through  the  centre  of  the  sphere,  fig.  1.  Since,  however,  the  visual 
rays  are  cot  coincident  with  the  luminous  rays,  the  apparent  posi- 
tion of  this  point  is  somewhat  changed.  Thus,  if  we  bring  the 
vertical  plane,  R  o,  fig.  1,  into  the  horizontal  plane,  the  luminous 
ray  will  coincide,  as  has  been  seen,  with  the  line,  r'  o',  ami,  conse- 
quently, its  point  of  intersection  with  the  sphere  will  coincide  with 
the  point,  i.  On  the  other  hand,  the  visual  rays  which  are  perpen- 
dicular to  the  horizontal  plane  will  coincide  with  parallels  to  c  o, 
when  brought  into  the  horizontal  plane.  This  latter  line  intersects 
the  sphere  in  the  point,  c ;  and  as  the  light  is  reflected  from  any 
surface  in  the  direction  of  the  visual  rays,  so  as  to  make  the  angle 
of  incidence  equal  to  the  angle  of  reflection,  if  we  divide  the  angle, 
toe,  into  two  equal  angles,  by  the  line,  n  o,  the  point,  n,  will  bo 
that  which  will  appear  to  the  eye  most  brilliantly  illuminated.  The 
positions,  n'  and  i',  in  the  vertical  plane  of  the  points,  n  and  i,  are 
obtained  by  letting  fall  perpendiculars  upon  the  line,  o  A,  repre- 
senting this  plane. 

In  shading  up  a  drawing  it  is  preferable  to  place  the  bright  or 
lightest  part  between  the  two  points,  n'  and  i',  a  more  pleasing  effect 
being  obtained  thereby.  When  the  sphere  is  polished,  as  a  steel, 
brass,  or  ivory  ball,  a  circular  spot,  of  pure  white,  must  be  left  about 
the  point  in  question.  When,  however,  the  body  is  rough,  as  is 
supposed  in  fig.  (g,  this  part  is  always  lighter  than  the  rest ;  but,  at 
the  same  time,  it  is  covered  by  a  faint  wash. 

In  the  case  of  a  hollow  sphere,  figs.  2  and  3,  we  have  to  bear  in 
mind,  not  only  to  indicate  the  position  of  the  bright  spot,  which 
is  projected,  in  the  same  maimer,  upon  the  luminous  ray,  a  b,  and 
lies  between  the  points,  n\  I',  but  also  the  point  in  the  cast  shadow, 


m 


THE   I'll  \(  1 


whk-h  .hookl  be  the  least  prominent.     Ti.  •■  found 

U>  be  at  '"•  nS-  3-  drawn 

..-.  into  the  same 
j.'jmr  H  |g    3 

Tbe  boQer  i»  rrpre*-  I  ta  Hi  furnace,  which 

i,  baiJt  •  rilh  s  diaphragm  pawing  down  tho 

middle  "•"<  and    gs- 

the  grata  to  pass  slot ..  than  '"  return  by  that 

U>  Um  right,  and  pa— 

■     .  ...  r,  full 

.   a  pipe 
pawn,-  '  teach.     In  ' 

water  Itroro.  -  •  as  not 

to  reduce  the  tempera-  :.  uI,on 

ita  introduction  intu  it. 

ted  as  half  full  of  w.itor.     It  should 
geotnl  .  ';  >ia]f  lu"  !  so 

that  a  greater  p  ntarior  may  !>>• 

Tin-  remain 
chambers,  is  suppose i  I  '"•     The  base  of  the 

is  of  brick.    Tne  foundations 
of  the  furnace  :. 

...  tain  which 

as  large,  ao  as  to  sequin  the  proper  skill  an  J  facility  of  treatment. 


SHADING  IN  I'.I.VX.- SHADING  IN  COLOURS 

PLATE    XXXIII. 

la* great  numl*r  of  drawir  ilariy  in  those 

I  drawing*,  and  intended  for  us,-  in  tetoal  eonstrao- 
shading  thi 
na  ink — son,  ring  1 1 » i -*  with  a  faint 

:  the  material.    The 
t  the  parts  in  relief,  and  ren- 
■  the  eye ;  a 
tiie  other  han  .  indicate  ..i"  what  material  they  are 

made.     This  duplex  arii-ti.  -  tin-  drawing 

much  ti.  bended,     A  drawing 

may  be  .  '    phut  il  first   to 

■hade  op  tho  various  surfaces  with  China  ink,  hat  b 

■  ording  t..  the 

lights  and  shades,  as  has  been  done  in  the  preceding  plate*,     The 

entire  surface  •  red  with  an  ■ 

wash  of  clour,  the  line  of  which  b  onal      11   must 

■n   in  flat  W*l  |   to  Hi"   Inatmctiona  given  in 

i 

ease*,  but  it  leaves  out  mod  In  the  effective 

without 

old  and  monotonous.    A  better  reeull  i-  obtainable  by 

•  China  ink  ■  depth,  and  by 

'■■iir.  laid  on  in 

.   with  the  Ch  produce 

put*,  whil-t  I1 


parts  ar,  l,»  pure 

the  bril- 
V  softer  and  I  .an  bo 

il  n.utra!  tint,  instead  of  tl 
ink,  for  the  pr 
difficult  to  mix,  ami  to  ke,  p  uniform. 

-kill  and  facility  in  the 
.in  may 
in  a  more  direct  and  vigorous  n 
out  altogether  the  preliminary  shading  with  China  ink,  and  laying 

time,  tl. 

material.     This  last  method  he*  the  merit  I 

of  the  drawing  a  richer  transiuoence,  more  warmth,  and  i 
tory  fulfilment  of  all  deeirabh 

I        ;;,  ra!.  all  drawings  intended  t..  be  shaded  should  \»-  d.!i- 
with  faint  graj  instead  of  ' 
outline  drawing;  the  faintnees  of  such  line*  avoids  the  ui 
of  making  them  very  fin.-,  and  their  greater  breadth  affords  a  much 
tide  to  the  shading-brush.     A  black  outline,  however  tine 
it  may  be,  always  produce*  a  too  sharp  and  I 
then  la  much  greater  ri-k  of  overstepping  it  in  laying  on  the 
■ 
373.  In  Plat.-  XXXIII.  we 
shaded  i  prising  the  m  ri  In  ma  in  con- 

struction. 

though  tin- wo... Is  are  naturally  verj  different  in  clour,  still,  in 
mechanical  lira'  indiscriminately  :   it  i-, 

have  said,  entirely  conventional. 

In  fixing  upon  these  colours,  the  obj<  ct  in  view  has  bean  to  avoid 
on,  and  to  employ  a  distinct  and  intelligible  colour  for 
the  representation  of  i  oopy  the 

natural  colour  in  all  It 

In  colouring  this  wooden  capital,  after  the  preliminary 
th.ns  which  we  have  mentioned,  for  determining  the  out 

the  shadow*,  |  '.  it    is  first   sha.l.sl   throughout   with 

China  ink.  and  when  this  shading  has  reach,  d  a  coincident  depth, 
and  is  thoroughly  dry,  the  whole  surface  is  to  be  covered  with  a 
light  wash,  which  may  he  a  mixture  of  gamboge,  lake,  and  China 

ink.  or  burnt  nmbi  r  alone.    The  colour,  in  fact,  should  be  analo- 

I.  Plate  X.  ;  it  should,  however,  ah 
fainter  than  In  that  example,  which  represents  the  mater,.. 
ti..n.  and   is,  therefor 

This  proceeding  may  be  easily  modified,  and  mi 
the  effect  of  the  second  method,  by  leaving  certain  parts  of  the 

incolound,  and  by  softening  off  the  -hade  in  th-- 
wh.re  the  light  i  tli  a  marly  dry  brush.     If,  however, 

the  draught-man  has  become   soinew  hat    familiarized  with  the  ttSS 
Of  the  hrii-h  and  the  mixture  of  the  colour-,  he  may.  Si  WS  have 
said,  omit    the  preliminary   shading  in    black,  by   modify  : 
■hade  as  laid  on,  mixing  the  China  ink  directly  with  the 
nlid  th.n  gradually  bringing  npthe  shades,  cither  accor.li: 

»\  -t.  in  of  Bat  washes,  ..r  the  more  difficult  o f  - 

.  •  ikl  n  in  lav  ing  on  tie  -■  shades  tO  commence  at  the 

part*,  and  then  to  c\er  ti. 


BOOK   OF   INDUSTRIAL   DESIGN. 


123 


quent  washes,  which  gradually  approach  the  bright  part  of  the 
object  ;  for  in  this  way  a  more  brilliant  and  translucent  effect  will 
bo  obtained. 

When  the  objects  are  of  wood,  it  is  customary  to  represent  the 
graining  in  faint  irregular  streaks,  care  being  taken  to  make  these 
as  varied  as  possible.  A  general  idea  of  the  effect  to  be  produced 
will  be  obtained  from  fig.  1. 

Following  out  these  principles,  the  draughtsman  may  proceed  to 
colour  various  other  objects  composed  of  different  materials,  merely 
varying  the  mixtures  of  colour  according  to  the  instructions  given 
in  reference  to  Plate  X. 

Fig.  2  represents  the  top  of  a  chimney  of  brickwork,  the  form 
being  circular.  In  this  external  view,  the  outline  of  each  brick  is 
indicated ;  and  to  render  them  more  distinct  from  each  other,  a 
line  of  reflected  light  has  been  shown  on  the  edges  towards  the 
light,  near  the  brighter  part  of  the  chimney.  Indeed,  it  is  generally 
advisable  to  leave  a  narrow,  pure  white  light  at  the  edges  of  an 
object  which  are  fully  illuminated,  as  it  gives  an  effective  sharp 
appearance. 

Fig.  3  represents  the  base  of  a  Doric  column  in  stone,  showing 
the  flutings.  This  being  an  external  view,  the  tint  to  represent  the 
stone  is  not  made  nearly  so  strong  as  for  the  sectional  stone-work, 
represented  in  Plate  X.  A  yellowish  grey  may  be  used  for  it,  made 
by  mixing  gamboge,  the  predominant  colour,  with  a  little  China  ink, 
adding  a  little  lake  to  give  warmth. 

These  three  examples  of  wood,  brick,  and  stone,  represent  bodies 


with  rough  surfaces,  and  which,  therefore,  can  never  receive  such 
brilliant  lights  as  objects  in  polished  metal ;  no  part,  indeed,  should 
be  entirely  free  from  some  faint  colour. 

Fig.  4  represents  a  nut  or  bolt-head  of  wrought-iron ;  and,  as 
we  have  supposed  it  to  be  turned  and  planed,  and  polished  upon 
its  entire  surface,  it  has  been  necessary  to  leave  pure  white  lights 
at  the  brighter  parts,  to  distinguish  the  surfaces  from  those  which 
are  rough  and  dull.  It  is  the  same  in  the  example,  fig.  5,  repre- 
senting the  base  of  a  polished  cast-iron  column,  and  in  the  lateral 
projection,  fig.  6,  of  polished  brass  upper  and  lower  shafUbearings 
or  brasses. 

We  would  hope  that  the  principles  of  shadows  and  shading,  ex- 
plained and  exemplified  in  the  last  two  chapters,  may  serve  as 
sufficient  guides  for  the  various  applications  which  may  present 
themselves  to  the  draughtsman — whether  his  skill  be  called  forth 
to  render  the  simple  effects  of  light  and  shadow,  or  to  produce  the 
gradations  of  shade  and  colour  due  to  roundness  or  obliquity  of 
surface — to  the  various  positions  of  the  objects  in  their  polished  or 
unpolished  state,  and  to  the  various  materials  of  which  they  may 


Thus,  it  will  be  understood,  that  although  two  objects  are  pre- 
cisely alike  in  material  and  form,  if  they  are  situated  at  unequal 
distances  from  the  spectator,  the  nearer  one  of  the  two  must  be 
coloured  more  strongly  and  brilliantly  than  the  more  distant,  more 
force  and  depth  being  given  to  the  darker  shades. 


CHAPTER  IX. 
THE    CUTTING  AND   SHAPING   OF   MASONRY. 

PLATE   XXXIV. 


374.  The  operation  of  stone-cutting  has  for  its  object,  the  pre- 
paring and  shaping  stones  in  such  manner  that  they  may  be  built 
up  into  any  desired  form  in  a  compact  and  solid  manner ;  great 
care  and  skill,  as  well  as  mathematical  knowledge,  is  more  parti- 
cularly required  in  the  preparation  of  stones  for  arches,  vaults, 
arcades,  and  such  like  structures. 

The  study  of  the  shaping  of  stones  is  based  entirely  upon  descrip- 
tive geometry,  being  indeed  but  a  particular  application  or  branch 
of  it,  and  in  it  have  to  be  considered  the  generation  of  surfaces,  as 
well  as  their  intersections  and  developments. 

In  proceeding  to  adapt  the  stones  to  the  position  they  are  to 
occupy,  the  mason  should  prepare  a  preliminary  drawing  of  the 
actual  size  of  each  stone,  as  well  as  a  general  view  of  the  entire 
erection,  indicating  the  joints  of  each  stone ;  these,  according  to 
the  various  positions  to  be  occupied  by  them,  are  called  key  stones, 
arch  stones,  &c. 

It  is  not  our  intention  to  give  a  complete  treatise  on  the  shaping 
of  masonry ;  but,  as  this  study  seems  to  belong,  in  part,  to  geome- 
trical drawing,  we  have  thought  it  quite  within  the  design  of  the 
present  work  to  give  a  few  applications,  sufficient  to  show  the  line 
of  procedure  to  be  followed  out  in  operations  of  this  nature. 


the  marseilles  arch,  or  arriere-vu„.ssure. 
Figures  1  and  2. 

375.  Wo  propose  to  prepare  the  designs  for  the  bay  and  arch 
of  a  door  or  window,  to  be  built  of  stonework,  the  upper  part 
being  cut  away,  so  as  to  present  a  twisted  surface,  analogous  to 
that  known  as  the  arriere-voussiire  of  Marseilles. 

This  surface  is  such  as  would  be  generated  by  a  straight  lino, 
c  a,  kept  constantly  upon  the  horizontal,  c'  k',  projected  vertically 
in  the  point,  c,  and  moved,  on  the  one  hand,  upon  the  semi-base, 
B  E  D,  of  a  right  cylinder,  having  c'  k'  for  its  axis ;  and,  on  the 
other,  upon  the  circular  arc,  F  e  a,  situated  in  a  plane  parallel  to 
that  of  the  base,  bed. 

The  lateral  faces,  f  b  l  n  and  A  R  Q  D,  of  the  bay,  are  vertical, 
and  are  projected  horizontally  in  f'  b'  and  a'  d',  fig.  2.  These 
faces  intersect  the  twisted  surface  at  the  curves,  F  B  and  A  D,  which 
we  shall  proceed  to  determine. 

For  this  purpose,  the  first  thing  to  be  done  is  to  seek  the  pro- 
jections of  the  straight  generator  line,  c  a,  as  occupying  different 
positions,  so  as  to  obtain  their  points  of  intersection  with  one  of 
the  oblique  planes. 


ay  rrmark,  thai  if  Up 

for  I  ioj.  J'  • .  of  !:.•    I.  and  • 

liraJ    p.— j««ti.-n»   of  Um>   g*t. 

. 

aaJM  liaea  abo  rui  the  cirvular  are.  I 

••!'  thb 

tbaae  bat.  an.: 

•ac  generatrix,  c  a.  and  eon 

I 

!  M  lines, 

.  A   M  /  I  D,  p 

I,  sou  U> avoid  :l. 

full  size,  it   a 

■ 

an  are  of  a  . 

■ 

over  the 
■mi  the 

iodivi- 

:  up. 

- 

the  key- 

i  with  the  tw 

th  i-.  the 

I 

\i.  n  /i  andoi,  •  - 

"BED  ami  r  • 

■ 

It  i*  the  eta  i  e  and  J  C,  in  which  lie  the 


:i«,  k  g  and  I  »    of  the 
led  hori- 
:  a'  t. 
- 
nhoiiUl  ■:  hashed  from  r 

•  joint),  ami  be 
tin  ii  taki 
from  an 
roughly  in  thi 

lane  the 

Tim-. 

:    in    front   view  ami 

:.ikes  a  paralleloniped,  of  wlm-h  the 
i  ..f  firvimwnliitiL'  the  two  parallel  I 
tin-  upper  part  of  the  key-stone,  and  of  «  hieh  th.-  1. 
equal  to  tin-  length,  i  it.    After  having  eat  ami  finished  the  two 
..  and  u'  r.  of  the  prism,  as  well  as  tin-  li  ■  • 
at  off  upon  tin-  anterior  face,  fig.  8,  the 
and  vertical  sidis.  (  o  and  a  r.  ami  then  the  obfiqtM  lims  o  f>  and 
p  {,  which, it  wHl  be  nuu-inl- 

ire.    Mr  ni-xt  seta  off  np.ui  a  tamp 
-  them  thence  opon  th 

:.  ti.'.  3.  at   ;i  0  and  h  I.     After  this  preliminary  marking 

out,  tin-  itoneentter  reduces  ami  takes  away  all  tin-  mati  rial  opon 

parallelopiped  which  lies  ootaide  tin-  tines,  i  1 

r  l ;  tl..  -  •  finished,  the  shape-d  it  upon 

them  id  i  at  n  h  ami  o  /.     In  order  that  thi  I 

•  inav  Ih-  more  easily  comprehended,  we  have  brought  the 
. 
if  projection, 
new,  H  will  '  ined;  for,  on  tin-  one 

hand,  we  h.i\.-  tin-  line,  tJ  y.  equal  to  k  k\  i  Ihe  thick. 

■  tin-  arch;  and.  on  tin-  other  hand,  nil  the 
other  dii  '!,lt  ,l"' 

>n  of  ;lu-  line,  d  I ,  can  be  determined  with  tin-  mi 

- 

tide  to  tin-  st i-utter  in  reducing 

■ 

affording  a  ti-  'on.  it  may  1h> 

ihould  In-  cut  in  tuch  a  manner,  thai  a 

l,v  t|„.  .  r  of  which  splits  from  the 

•:,.•   latter    from  tin-    | 

ither  of  tin-  tw 

ted  in  their  full  dimei 

. 

trail  l  to  thi- 1 
Thus,  to  obtain  tin-  actual  dhneni  •..•joint 

1  at  0  h,  with  tin-  poll 

..  u;  u  i/-,  h  w.  *«  a»  to  reproduce  tlio 
...  u,  h,  at  u\  h',  V,  upon  tin-  vertical,  o"  ir ;  then,  bj 


BOOK  OF   INDUSTRIAL  DESIGN. 


off,  ft"  K',  equal  to  n'  h',  fig.  2,  and  joining  the  points,  h'  n",  fig.  7, 
we  get  the  inclination  of  the  generatrix  line,  if  h',  which  is  project- 
ed vertically  at  n  h,  fig.  1.  The  form  of  the  joint  face  is  completed 
by  drawing  the  horizontal  lines,  o1  w ,  h'  z',  y'  i',  and  the  verticals, 
■u  v'  and  z'  y',  which  last  are  already  given  full  size  in  fig.  6.  It 
will  be  observed  that  fig.  7  is  on  the  plate  removed  a  little  to  the 
right  of  the  vertical,  oa  w  ;  but  this  is  a  matter  of  no  importance,  and 
is  merely  done  for  convenience  sake. 

The  same  system  of  auxiliary  projections  is  applicable  to  the 
determination  of  the  dimensions  of  the  other  face  of  this  piece — 
namely,  that  projected  at  m  g,  which  is  brought  round  to  the  hori- 
zontal, m'  g2,  and  drawn  with  full  dimensions  in  fig.  8 ;  only,  for 
this  last  face,  it  is  necessary  to  bear  in  mind  the  portion  of  the  line 
of  intersection  of  the  sides  with  the  arched  part  which  it  contains, 
and  which  is  obtained  in  its  actual  proportions,  as  at  c?  m3,  by 
means  of  a  template  formed  to  the  curve,  a"  m",  in  fig.  1.  The 
stone,  T,  beneath,  of  course,  contains  the  remainder  of  the  inter- 
sectional  curve. 

The  methods  just  explained,  in  regard  to  the  shaping  of  the  key- 
stone and  one  of  the  corner-stones,  may  be  extended,  without  diffi- 
culty, to  the  remaining  portions  of  this  Marseilles  arch. 

In  this  application  it  has  been  necessary  to  determine  the  propor- 
tions of  the  twisted  bay  of  the  arch,  as  well  as  the  faces  of  the 
joints ;  but  in  the  more  general  case  of  straight,  bays,  such  as  that 
represented  in  fig.  I1",  the  operations  are  considerably  simplified, 
and  the  designer  has  merely  to  attend  to  the  form  of  the  joint  faces, 
making  use,  for  this  purpose,  of  the  auxiliary  projections,  as  above 
described.  The  delineation  of  the  various  parts  of  this  figure  pre- 
senting no  new  peculiarity,  it  need  not  further  detain  us. 

378.  Let  it  be  proposed  to  delineate  a  circular  vault  with  a  full 
centering,  bounded  by  two  plane  surfaces  oblique  to  its  axis,  figs. 
9  and  10.  This  example  is  taken  from  the  entrance  to  the  tunnel 
on  the  Strasbourg  Railway,  near  the  Paris  terminus,  and  it  is  a  form 
frequently  met  with  in  the  construction  of  railways. 

In  the  representation  of  this  vault,  we  have  supposed  one  of  the 
oblique  planes  to  be  parallel  to  the  vertical  plane  of  projection!  and 
it  consequently  follows  that  the  axis  of  the  arch  is  inclined  to  this 
plane. 

Let  a  B  he  this  axis,  and  c  D  the  horizontal  projection  of  a 
plane  at  right  angles  to  it ;  with  the  point,  e,  as  a  centre,  describe 
the  semicircle,  cad,  representing  the  arch  in  its  true  proportions, 
as  brought  into  the  plane  of  the  picture.  Let  us  suppose  this 
semicircle  to  be  divided  into  some  uneven  number  of  equal  parts, 
as  in  the  points,  a,  b,  c,  d,  e,f ;  through  each  of  these  points  draw 
straight  lines,  passing  also  through  the  centre,  E,  and  representing 
the  joints,  a  g,b  h,  c  i,  of  the  arch  stones,  being,  of  course,  normal 
to  the  circular  curvature  of  the  arch,  and  being  limited  in  depth,  as 
we  shall  suppose,  by  the  second  outer  semicircle,  g  i  I,  concentric 
with  the  first.  Each  of  these  joint  faces  intersects  the  centering 
of  the  arch  in  a  straight  line  parallel  with  its  axis,  and  the  horizon- 
tal projections  of  these  intersections,  as  seen  from  below,  are  ob- 
tained simply  by  drawing  through  the  points,  a,  b,  c,  d,  lines  parallel 
to  the  axis,  B  a;  these  last  extend  as  far  as  the  vertical  plane,  a  e, 
which  bounds  a  portion  of  the  vault.  The  external  faces  of  the 
key  and  arch  stones  are  limited  by  straight  vertical  lines,  such  as 
m  h,  i  n,  oj,  and  horizontals,  as  m  i  and  n  o. 


We  have  now  to  obtain  the  projections  on  the  vertical  plane, 
fig.  10,  of  the  intersection  of  each  of  the  arch  stones  by  the  plane, 
a  e. 

We  may  remark,  in  the  first  place,  that  since  this  plane  is 
oblique  tp  the  axis  of  the  cylindrical  arch,  it  produces  an  elliptical 
section,  having  for  its  semi-transverse  axis  the  length,  c'  a,  and  for 
its  semi-conjngate  axis,  the  length,  a  b  ,  equal  to  the  radius,  a'  e. 
As  much  of  this  ellipse  as  is  required  is  drawn  according  to  one 
or  other  of  the  many  methods  given  (53,  et  seq.) — say  as  at  c'  is  b' 
fig.  9,  which  curve  is  reproduced  at  c"  o"  a",  in  the  elevation, 
fig.   10. 

If  we,  in  like  manner,  obtain  the  projection  of  the  semicircle,  F  i  I, 
which  limits  the  radial  joints,  we  shall  also  obtain  the  portion  of  an 
ellipse,  f"  g"  i\  and  we  have  further  merely  to  project  the  points, 
a',  b',  c',  upon  the  first  ellipse,  in  a"  b"  c" ;  as  also  on  the  second 
one,  the  points,  g",  h",  i",  corresponding  to  g  ft  and  i.  The  straight 
lines,  f"  c",  g"  a",  h"  b",  i"  c",  represent  the  intersections  of  the 
faces  of  the  arch  stone  joints,  with  the  plane,  a  e. 

The  vault  being  supposed  to  extend  no  further  back  than  the 
plane,  c  D,  it  will  be  necessary  to  represent  the  intersection  of  this 
last  with  the  arch  stones  which  extend  thus  far  upon  this  plane, 
c  D.  We  have,  therefore,  to  project  the  elliptic  curves,  c'"  b'"  c" 
and  f"'  g'"  i",  corresponding  to  the  quarter  circles  of  the  radii, 
F  B  and  c  b.  As  the  arch  stones  cannot  extend  the  entire  length 
of  the  vault,  they  are  limited  by  planes,  M  N,  perpendicular  to  the 
axis,  and,  consequently,  parallel  to  c  D.  so  that  the  projections  of 
these  joints  will  be  but  repetitions  of  portions  of  the  same  elliptic 
curve ;  care  is  taken  so  to  dispose  the  blocks  of  stone,  that  no  two 
joints  form  a  continuous  line,  the  joints  in  one  course  being  brought 
between  those  in  the  adjacent  ones,  as  is  customary  in  all  brick  and 
stone  work. 

379.  We  have  now  to  determine  the  intersection  of  the  oblique 
plane,  a  g,  with  the  remaining  half  of  the  same  circular  vault,  and 
then  to  obtain  the  projection  of  this  intersection  upon  the  vertical 
plane. 

The  plane,  A  G,  also  produces  an  elliptical  section  of  the  van't ; 
this  is  represented  at  g'  gt,  as  brought  into  the  picture  in  the  auxiliary 
diagram,  fig.  11,  which  gives  its  actual  proportions ;  the  semi-trans- 
verse axis,  g'  o,  of  this  ellipse  is  equal  to  G  A,  and  its  semi-conjugate 
axis  is  equal  to  the  radius,  a'  b,  of  the  vault. 

After  having  divided  this  curve  into  a  certain  uneven  number  of 
equal  parts,  draw  normals*  p  u,  q  v,  r  x,  s  y,  and  I  z,  through  I  ho 
points  of  division  representing  the  joints  of  .the  arch  stones,  the 
remaining  sides  of  the  external  faces  of  which  are  limited  b)  hori- 
zontals and  verticals,  as  before. 

If  the  vault  is  supposed  not  to  extend  beyond  the  plane,  a  g, 
the  arch  stones  will  have  to  be  shaped  as  facing  stones,  and  their 
joints  will  require  to  be  set  off  upon  the  first  ellipse,  g'  q  l,  and  to 
be  limited  by  the  second,  h'  q*  C,  obtained  from  the  intersectional 
plane,  H  i,  drawn  parallel  to  A  G ;  by  drawing  straight  lines  from 
the  points  of  division  obtained  upon  the  ellipse,  g'  q  I,  to  the  centre, 
o,  we  obtain  the  points,  p',  q*,  r\  s',  of  intersection  of  these  line? 
upon  the  second  -ellipse,  and  the  straight  lines,  p  p\  q  q',  r  r3,  s  sa,  fe- 
presenting  the  intersections  of  the  arch  stones  with  the  inside  of  the 

•  A  line  is  said  to  be  normal  to  a  curve,  when  it  is  perpendicular  to  a  t  intent  t« 
the  curve  passing  through  its  point  of  intersection  with  the  curve  (73). 


m 


iaaa  sre  projected  horizontally  in  f  /,  cr*  o*. 
.  fig.  9,  si,.  -.!•»«■.  bxua  toe  diagram  is 

Mp|>arU  to  U  f  the  vault,  aa  seen  from  below ;  the 

two  dasgram*,  figs.  9  and  It.  wiU  reader  the  determination  of  the 
vortical  projection,  fie;.  10.  very  easy,  the  asm*  lines  there  being 
d— igsslrd  by  the  — e  letters. 

To  limit  the  arch  lacing  atones,  and  unite  them  coavenW  r 
the  regular  unit—  of  tin-  vault,  th«  y  must  be  cut  by  planes,  aneh 
aa  J  I  and  L  r,  fig.  9,  psrpendirolar  to  the  aii.%  A  a.     TV 
tioaa  of  thee*  planea  with  the  vault  produce  |-.rti,.n- 
are  projected  aa  ellipses  in  fig.  1 1,  such  as  l'  if  v  and  v'  r*  x'.  for 
the  inside  of  the  vault,  and  >'  q  «'  and  l'  s'  ij.  fbf 
trccnitics,  them  various  ellipses  corresponding  to  the  radii,  c  ■  and 
r  a.     The  joints  of  tbeae  stones  are  finally  completed  by  planes, 
each  aa  t  r*  a  Q,  fig.  II.  passing  through  the  axi-.  a  b,  and  through 
horizontal  lines.  T  z'  and  o  a,  in  the  vault,  the  latter  and  i. 
of  which  only  ia  risible  in  tii-  :    10. 

380.  In  constructing  this  vault,  it  is  necessary  to  make  detailed 
drawing*  of  each  part:  •»  ing  the  dimensions  of  all  the 

foes*,     In  las,  IS  :■  16,  va  !.^-.,-  rapreaaxted  oaa  ••;  m  -<•  a.-.-h 
at  now,  O.  in  pun  and  elevation,  aa  detached  from  I 
10,  and  showing  more  particularly  such  lines  as  are  not  apparent  in 
Thus,  in  these  views  may  be  distinguished: — 

bee,  ■  q  r  x,  which  i«  :  .ontally 

upon  the  line  of  the  plane,  a  g  ;  mil  inhered, 

intersect*  the  vault  at  the  elliptic  cur  -  q  r. 

3d.  The  fao  M  edge,  x  r.  is 

:   upon  the  same  plane,  c  A,  at  x   - 

:    upon   the  line,  r'  r',  parallel  lor,  i;  and 

•  r  edge,  r  r*,  the  line  of  int»  n  I  th  the 

Hat,  finally,  the 
upper  and  fourth  edge,  x  w,  is  projected  at  . 

3d.  Tiit  second  joint  face,  r  q  /  w,  U  opposite  to  the  first,  and 

4th.  Toe  face,  n  «  z  t,  lhi>  horizontal   ; 

.   ;  this  face  is  situated  in  a  plane  pas  the  axis 

of  the  vault,  and  is  additions.'  :i  the  diagnu. 

on  the  radius,  r  q*. 

6th.  The  species  of  dovetail  joint,  q  <f  t  z  r*  r,  of  «. 
edge*,  o  o*  and  r  r*.  are  projected,  as  has  been  Men,  at  q  q*  and 
.ilst  the  sides,  q  r  and  z  r\  are  similarly  projected  at  q"  r 
and  z  r',  and  : 

6th.   I. 
render  an  account  by  mean-  eh  are 

invariably  the  same  for  the  same  points,  altii 
mark*  are  snperadded  to  obviate  eoi  various 

nave  added  the  subsid. 
of  the  block  in  the  plane,  ir.u  I  • 
picture  ;  we  have  thus  the  actual  pr  ; 
in  the  planea,  a*  r*  sn  1 

■> ,  it  is  sufficient  to  *  I   -a]  distances  I 

line,  o  o,  of  the  elevation,  figs.   II  and   13,  obtaining  in  this  man- 

•  instance,  the  points  r*,  7'. 
■ '.    '       and  x. 

"Ni  example*  chosen  for  this  plat.     \  \  \  I V       .  .rnoine  the  more 


difficult  problems  and  applications  met  with  in  the  shaping  aad 
arrangement  of  stonework,  and  will  make  the  student  aoqn 
with  the  operations  upon  which  design*  for  these  purpose*  are 
based,  aa  wed  aa  with  the  general  method*  to  be  adopted  in  obtain, 
ing  oblique  projections  by  the  employment  of  auxiliary  projections, 
taken,  a*  it  were,  in  planes  parallel  to  the  different  surfaces,  and 
then  brought  into  the  plane  of  the  picture ;  this  system,  at  the  same 
time,  being  of  much  use  in  ascertaining  the  exact  proportions  of 
various  surfaces,  such  as  the  joints  of  masonry. 


RUI  .  MTHAL  DATA. 

BYDBACUC    MOTORS. 

3S1.  Tin-  fall  of  a  stream  of  water  varies  with  the  locality,  and 
rent  kinds  of  hydraulic  motors, 
which  are  denominated  as  follows,  according  to  their  several  pe- 
culiarities. 

Undershot  water-wheels,  which  receive  the  water  below 
.-.res,  and  the  buckets  or  floats  of  which  pass  through  an 
enclosed  circular  channel,  at  the  part  where  the  water  acta  upon 
them. 

i.  Overshot  1  iuch  receive  the  water  from 

above. 

Thirl  vertical  axes,  known  as  turbines,  and  which 

are  capable  of  working  at  various  depths. 

Fourth.  Wial  h  plane  floats  or  buckets,  receivTig 

the  wat>  -   and  working  in  enclosed  channels, 

through  a  portion  of  their  circumference. 

irved  buckets. 
anted  on  barges,  and  suspended  in 
the  currenL 

U5DERSH0T   WATER-WHEELS,   WITH   PLANE    FLOATS   A5D    A 
CIRCULAR    CHA55EL. 

mtageous  arrangemeot  that  can  be  adopted 

in  the  construction  of  an  and  htfa  plane  floats, 

riving  in  an  enclosed  circular  channel,  is  that  in  which  the 

-  formed  by  an  'nd  when  the  bottom 

of  this  -  J  tu.,  or  about  8  inches,  below  the  general 

Lei  it  bv  re-juirvd  to  determine  the  width  of  an  undershot  water- 
ing data: — 

:  1<H)  litre*  per  second. 
l.Jl  is  2  475  mi 
Thini.  '   the  water  at  the  sluice-gate  is  to  1- 

WIDTH    OF    THE    WHEEL. 

':«■  seen,  in  the  table  at  page  113,  that,  with  an  outlet  of 

•23  in  depth,  a  discharge  can  -  of  water  per 

for  a  width  of  1   metre;  consequently,  the  width    to  be 

1  the  sluice,  to  enable  it  to  discharge  1,200  litres  per  second, 

should  be— 

1200  ■+-  188  =  fi  39  metres. 


BOOK   OP    INDUSTRIAL   DESIGN. 


DIAMETER  OF    THE    WHEEL. 

383.  The  diameter  to  be  given  to  a  wheel  of  this  description  has 
not  been  accurately  determined,  because  it  has  not  a  direct  influence 
upon  the  useful  effect  that  may  be  obtained  from  it.  Nevertheless, 
it  is  manifest  that  it  should  not  be  too  small ;  for  in  that  case  the 
water  would  be  admitted  too  nearly  in  the  horizontal  line  passing 
through  the  centre,  or  even  above  it,  which  would  cause  great  loss 
of  power.  Neither  should  it  be  too  great,  for  in  that  case  the  ex- 
aggerated dimensions  would  but  involve  an  increased  bulk  and 
weight,  and,  consequently,  a  greafer  load  and  more  friction,  without 
any  compensating  advantage. 

In  general,  for  a  fall  of  from  2  to  3  metres,  it  is  advisable  to  make 
the  extreme  radius  of  the  wheel  at  least  equal  to  the  mean  height 
of  the  fall,  augmented  by  twiee  the  depth  of  the  water  upon  the 
edge  of  the  outlet. 

Thus,  in  the  case  before  us,  the  height  of  the  fall  being  limited 
to  2-475  m.,  the  outer  radius  of  the  wheel  should  Tiot  be  less  than 
2-475  m.  plus  twice  the  depth  of  the  overflowing  body  of  water 
when  at  its  fullest — say  '6  m. ;  that  is  to  say,  in  all,  3075  m.,  which 
corresponds  to  a  diameter  of  6-15  metres. 

Water-wheels,  on  the  same  system,  with  a  fall  of  water  of  from 
2-6  to  2-7  metres,  have  often  an  extreme  diameter  no  greater  than 
this. 

VELOCITY   OF    THE    WHEEL. 

384.  Theoretically  speaking,  the  velocity  which  it  is  convenient 
to  give  to  an  undershot  water-wheel  should  be  equal  to  half  that 
due  to  the  height  of  the  overflow  of  the  water ;  that  is  to  say,  equal 
to  from  1-  to  1-1  in.  in  the  present  case.  Nevertheless,  practice 
shows  that  this  rule  may  be  departed  from  without  inconvenience, 
and  the  wheel  may  be  made  to  attain  a  velocity  of  from  1*5  to  l"6m. 
per  second  at  pleasure,  which  is  a  very  great  advantage  in  many 
circumstances. 

If  the  wheel  makes  three  turns  per  minute,  the  mean  velocity  at 

the  outer  circumference,  and  at  the  edges  of  the  floats,  will  be — 

615  x  31416  x  3 
. s; =  1-021  m.  per  second. 

Thus,  when  the  height  of  the  overflow  is  -24  in.,  the  correspond- 
ing velocity  of  the  water  being  2-17  m.  nearly,  as  shown  in  the 
table  at  page  94,  which  gives  the  heights,  2356  and  24-67  cent., 
therefore,  the  ratio  of  the  velocity  of  the  wheel  to  that  of  the  water 
is  -47  :  1. 

If  the  height  of  the  overflow  were  reduced  to  -15  m.,  which  sup- 
poses that  the  discharge  would  only  be 

101  litres  x  6-32  m.  =  638  litres  per  second, 
the  corresponding  velocity  of  the  water  would  not  be  more  than 
1-72 ;  and  in  this  case,  the  ratio  of  the  velocity  of  the  wheel,  sup- 
posing it  to  be  still  the  same,  to  that  of  the  water,  would  be — 
•595  :  1. 

NUMBER  AND  CAPACITY  OF  THE  BUCKETS. 

385.  Although  the  number  of  buckets  cannot  be  determined  in 
accordance  with  any  exact  rule,  it  is,  nevertheless,  of  importance 
that  their  pitch  should  not  be  much  greater  than  the  depth,  or 
thickness,  of  the  overflowing  body  of  water  acting  upon  them.     It 


is  also  necessary  that  the  number  of  the  buckets  should  be  divisible 
by  that  of  the  arms  of  the  wheel,  so  that  the  whole  may  be  put 
together  conveniently. 

Now,  since  the  outer  circumference  of  the  wheel  is 
G15  x  31416=  19-32  metres, 
we  can  very  conveniently  give  it  8  arms  and  64  buckets ;  and  the 
pitch  of  these  last  will  be  -32  m.  With  this  distance  between  the 
buckets,  there  should  not  generally  be  a  greater  depth  of  overflow 
than  -25  or  -26  m. ;  because,  at  -27  m.  the  water  will  begin  to  choke, 
as  it  will  not  be  admitted  easily  into  the  buckets,  and  will  rebound 
against  the  interior  of  the  channel,  giving  rise  to  a  continual  shak- 
ing action. 

Thus,  then,  in  determining  the  number  of  buckets  for  an  under- 
shot water-wheel,  receiving  the  water  from  an  overshot  outlet,  it  is 
necessary  to  calculate  the  spaces  between  them,  so  as  to  be  about 
a  third,  or  at  least  a  fourth,  greater  than  the  depth  of  the  water  at 
the  outlet,  whilst  their  number  must  be  divisible  by  the  number  of 
arms  of  the  wheel. 

For  water-wheels  of  from  3-5  to  4-75  metres  in  diameter,  six 
arms  for  each  rim  or  shrouding ;  for  wheels  of  5  to  7  metres  in 
diameter,  there  should  always  be  eight  arms  for  each  shrouding; 
and  the  number  of  arms  should  obviously  increase  for  wheels  of 
greater  diameters  than  7  metres,  of  which,  however,  there  are  but 
few  examples. 

With  regard  to  the  capacity  of  the  buckets,  and  the  channel, 
taken  together,  it  should  be  equal  to  at  least  double  the  volume  of 
water  discharged.     Therefore,  on  this  basis,  we  can  always  easily 
determine  the  depth  to  be  given  to  the  buckets,  when  the  maximum  ' 
discharge  is  known. 

Thus  allowing,  in  the  present  instance,  the  maximum  discharge 
to  be  1,340  litres  per  second,  instead  of  1,200,  since  the  velocity  at 
the  outer  circumference  is  1-021  m.  per  second,  the  number  of 
buckets  contained  in  this  space  is  equal  to 
1-021  -=--32  =  3-19. 
Then— 

T340  -i-  3-19  =  -43  cubic  metres  nearly, 
the  quantity  which  should  be  in  each  bucket  during  thi>  revolution 
of  tin-  wheel.  If,  then,  the  capacity  is  to  be  double  this,  it  will  bo 
equal  to  -86  cubic  metres.  The  product,  however,  of  the  width, 
6-38  m.,  of  the  wheel,  multiplied  by  the  space  between  two  consecu- 
tive buckets,  -32  m.,  is  equal  to  2-022  m. 

We  have,  then,  -86  -=-  2-022  =  -42  m.,  for  the  depth  of  the 
buckets.  The  distance  between  the  buckets,  however,  is  not  the 
same  at  the  inside  as  at  the  extremities,  and  the  capacity  is  also 
further  diminished  by  the  thickness  of  the  sides  of  the  buckets,  and 
by  the  inner  portions,  which  make  an  angle  of  45°  with  the  outer 
portions.  For  these  reasons,  the  depth  should  be  somewhat 
increased.  When  the  discharge  of  water  is  considerable,  and  we 
are  limited  as  to  the  width  of  the  wheel,  it  is  preferable  to  do  awai 
with  the  inner  inclined  portion  of  the  buckets,  as  indicated  in  the  ■ 
drawing,  Plate  XXXVI.,  prolonging  them  considerably  towards 
the  centre  of  the  wheel. 

USEFUL    EFFECT   OF    THE    WATER-WHEEL. 

386.  The  absolute  force  of  a  stream  of  water  is  the  product 
of  the  water  discharged  per  second,  expressed  in  kilogrammes,  bv 


THE    I 


la»  >...».!  •..'!»«•  U/1  erpieeai  I  ia  aita,  or  tit*  wri^l  In  p., nod* 
lafcet. 
T!.c«.  >l«i  the  diarharg*  h>  UOOUlraaor  kBoff-  pec  eeoood,  and 
•I  I-  i.+l  of  It. 

.imrir.  •  llic  .  V.l.nuiy 

.md  3217  -I-  75  =  43  I 

U'  .t.jr...i    Whl  ii  v«.   .   .    I  .Iru.lc-l.  arr   r.i|.  .  !     .■  .-   lr    in 

ovi«» 

fail,    nr   the 

■ 

:  by  a  vertical  sluice-gate,  with 

•   i ■.;. .  i.  aaatro.  ■■■■■■<  a:  tl..  hui  •  t. 

:     v  ;  alM.\« 

nt  |  .._•••  1 1 1.  of  tin-  diachi 

b  tba  quantity  which 
■■apea  at  an  orifice    1 1  tn.  in  hi  i^ni.  by  1  I  A  with 

880  x  -5 

•  v  partt. 

**   If"  ■'  .'in-utii- 

I 

■ 

ild  In-  counterbalanced  by  the 
■ 

1    of  the 

Don  ii  will  be 

■ 

'  ll  fall. 

•  *  ti.»t  the  depth  of  tl 
•""T  '"  '  -  much 

!  I 

mutt  be  add 
'  the  wale*  in  1 1 ■.-  dm  t  i-  bh>d 

' 


Ing  all  tli<  x-  quanti:. 

■•  +-   03  +  -01  +  -01)  =  4305  m. 

IV  ■  and  lli.' 

width  ■  ' 

•  •  with  contraction  from  the  tali 
■  again  to  bV 

II  I,  tip 

* 


:    1  ISO        I 

l  M  in.  for  tin'  width 
what  I. 
Tba  .1.  ptfa  of  Um  be  lined  thu»  i — 

8  x  -I M  in. 


.f  the 


=  Jl  I  in.; 


1 

lently,  the  internal  diameter,  il,  of  th<  i..a— 

d'  ::  m. 

Py  ii'  depth  ali. hi  n  fifth,  which  will   maka  it 

to  Ih-  allowed  berwi  >  n  tin- 
interna]  i-i rx-«i 1 1 1 "  J  to — 

19*174  nx, 
(livi.li: 

18-174  ,     , 

rater-wheel,  howovi  ■ 

and  If  ii  i-«  inU  ndod  to  maka  lha 
■hroudin  thai  lha 

ihiiiiIk  r  "I  buck)  la  bo  divisible  by  S;  it  will,  th< 

to  havi     I  17.  an. I   in   llii- 

t«> .  n  each  will  Ih-  reduced  to — 

l  _:  i  .  i  in. 

Ii  iniw  merely  nana  wheel;  for  tlii»  porpi 

thd  lie. 

il  ii  ill.  n  to  Ih.  divided  into  I 
and  ra.lii  are  drawn  ii  nl  af  diviaion, 

\  \  \\  I  .   on   ■  .   outward  from   the 

I    equal  l<.  a  lit  1 1 « -  DOM  llinn  Imlf  Ui<> 

depth  of  the  b  to  indicau   the  bottoma  of  il». 

Tl aairuutad  in  llii»  iii.iiiiht,  may  give 

,,iV7'i  ..r  mi  par  .-''lit.  ..i  tl..  wain  r. 

N..w  il.  I.. — 

v  .il  li..r».  H-|H.wrr. 

1 1  in  of  wafer. 

wilh  .•■•rtainly. 
tl.ai  the  |h.».  r  inarntttad  by  tlii-.  wheal  wU  I 

tO  ~  I  ..r  '. 

■ 
wbiofa  tliin   «  .nike  per 

niinuic  ia — 


BOOK   OF    INDUSTRIAL   DESIGN. 


129 


GO  -~  4-305  x  314  =  4-44, 
since  its  velocity,  r,  is   1   metre  per  seeond,  or  60  metres  per 
minute. 

In  tracing  out  the  preceding  solution,  it  will  have  been  seen  that 
the  width  to  be  given  to  the  wheel  is  1-76  m. ;  a  much  less  width 
might  have  been  obtained,  by  making  the  wheel  revolve  faster,  and 
by  augmenting  the  velocity  of  the  water  also.  Let  us  suppose,  for 
example,  that  the  question  has  to  be  solved  on  the  hypothesis,  that 
the  velocity  of  the  water-wheel  is  to  be  1-5,  instead  of  1  metre,  per 
second;  it  will  then  be  necessary,  in  order  that  the  water  may 
escape  from  the  orifice  at  double  this  velocity,  that  it  be  equal  to  3 
metres  per  second. 

For  this  velocity,  the  height  of  the  upper  level,  above  the  centre 
of  the  orifice,  should  be  -46  in. 

Allowing  -06  m.  for  the  height  of  the  open  part  of  the  sluice-gate, 

the  whole  height  above  the  wheel  will  be 

•46  +  -03  +  -02  =  -51  metres; 

consequently,  the  outer  diameter  of  the  latter  should  bo 

d  =  4-56  —  -51  =  4-05  metres, 

the  width  of  the  sluice-gate,  or 

•140 

w  =  -^ ^ =  I'll  metres, 

■06  x  3  x    -7 

and  consequently  the  width  of  the  wheel 

=  1-11  +  -10  =  1-21  metres. 

This  width,  it  will  be  seen,  is  considerably  less  than  that  first 
calculated.  This  wheel,  however,  which  is  narrower,  and  revolves 
at  the  rate  of  1-5  metres  per  second,  will  not  be  capable  of  trans- 
mitting so  great  a  useful  effect,  by  four  or  five  per  cent.  Never- 
theless, it  may  be  preferable  in  many  circumstances  to  adopt  this 
lesser  width,  either  to  render  the  wheel  lighter  and  less  costly  in 
construction,  or  to  avoid  the  necessity  of  much  intermediate  gear 
between  the  wheel  and  the  machinery  to  be  actuated.  Thus,  it  is 
evident  that  tins  wheel  should  make 

(60  x  1-5)  -=-  (4-305  x  314)  =  666  revolutions  per  minute, 
whilst  the  first  wheel  only  made  4-44.., 

The  other  parts  of  the  wheel  are  proportioned  according  to  the 
above  rules  ;  they  will,  however,  differ  but  slightly  from  those  of 
the  first  wheel. 

The  proportions  of  the  water-wheel  might  still  be  otherwise 
modified;  thus,  the  depth  of  water  at  the  outlet  might'be  allowed 
to  be  greater  than  that  taken  for  a  basis  in  the  preceding  cal- 
culations. Thus,  the  outlet  might  be  opened  to  the  height  of 
•1  m.  instead  of  only  -06  m. :  in  this  case,  the  width  of  the  outlet 
and  of  the  wheel  would  be  much  less.  But  this  arrangement 
would  have  many  disadvantages,  for  it  would  be  necessary  to  make 
the  buckets  more  open ;  that  is  to  say,  the  angle  made  by  the 
outer  portion  of  the  bottom  of  the  bucket  with  the  tangent  to  the 
circumference  passing  through  its  extremity,  instead  of  being  15° 
or  16°,  as  is  usual,  would  have  to  be  30°  or  32°;  the  buckets 
would  have  to  be  deeper  and  more  capacious  ;  they  would  empty 
themselves  sooner :  from  all  which  causes  would  follow  a  decrease 
in  the  useful  effect  given  out,  which  might  reach  even  to  15  per 
cent 

It  is  true,  on  the  other  hand,  that  the  width  of  the  outlet  would 
be  reduced  to  1  metre,  supposing  the  wheel  to  revolve  at  the     | 


rate  of  1  metre  per  second,  and  that  it  would  not  he  more  than 
■67  m.  when  the  wheel  revolves  at  the  rate  of  1-5  m.  per  second  ; 
in  which  case,  the  depth  of  the  buckets  would  be  about  -34,  and 
the  spaces  between  them  -4  m.  each. 

It  will  be  easily  conceived  that  such  an  arrangement  cannot  be 
advantageously  adopted,  except  where  there  is  plenty  of  water  to 
spare,  and  when  the  constructor  is  limited  as  to  the  width  of  the 
wheel. 

WATER-WHEELS   WITH   RADIAL   FLOATS. 

388.  In  old  mills  we  sometimes  meet  with  water-wheels  which 
have  plane  floats  placed  radially,  working  in  straight  inclined  chan- 
nels, with  a  vertical  outlet  more  or  less  distant  from  the  centre  of 
the  wheel. 

These  wheels  generally  give  out  25  to  35  per  cent,  of  useful 
effect  of  the  absolute  force  of  the  stream.  In  them  the  floats  are 
three  or  four  centimetres  clear  of  the  sides  of  the  channel ;  when 
a  greater  space  than  this  is  allowed,  the  useful  effect  is  sensibly 
diminished.  Generally,  the  width  of  such  wheels  is  equal  to  that 
of  the  outlet. 

At  the  present  day,  water-wheels  are  never  constructed  with 
plane  floats  arranged  in  this  way.  When  a  wheel  is  required  to 
have  a  great  velocity,  it  is  preferable  to  construct  it  to  work  in  an 
enclosed  circular  channel,  and  to  receive  the  water  from  above,  or 
from  an  orifice  with  a  sufficient  column  above  it,  to  give  the  propor- 
tionate velocity  to  the  water. 

Such  wheels  are  constructed  in  the  same  manner  and  with  the 
same  care  as  undershot  water-wheels ;  in  fact,  they  do  not  differ 
from  the  latter,  except  in  that  these  receive  the  water  from  an  open- 
topped  or  overshot  duct.  The  useful  effect  given  out  by  them 
varies  from  40  to  50  per  cent.,  according  as  the  sluice-sate  is  more 
or  less  near  to  the  upper  level  of  the  water.  Thus,  the  nearer  the 
channel  approaches  to  the  upper  level,  the  more  Iiko  the  wncel 
becomes  to  a  commoi,  undershot  one,  and,  in  consequence,  the  use- 
ful effect  is  greater. 

In  the  construction  of  a  water-wheel  of  this  kind,  the  same  rules 
are  followed  as  are  already  laid  down  for  common  undershot  wheels 
with  open  outlets. 

Thus,  let  it  be  proposed  to  construct  a  wheel  for  a  fall  of  1-75 
metres,  and  with  a  discharge  of  440  litres  of  water  per  second ;  let 
the  centre  of  the  outlet  orifice  be  at  -4  m.  below  the  upper  level, 
and  the  height  of  the  orifice  itself,  -15  m. 

By  referring  to  the  table  on  page  111,  it  will  be  seen  that  the 
discharge  of  water  through  an  orifice,  under  these  circumstances,  is 
255  litres  per  second  for  a  width  of  one  metre,  and  it  will  therefore 
be  evident  that  the  wheel  should  have 

440 

ijgg  =  1-72  metres  in  width. 

The  velocity  of  the  water  at  the  sluice-gate,  corresponding  t.. 
the  column  of  -4  m..  is  2 -81  12  per  seeond ;  consequently,  if  we  make 
the  velocity  of  the  wheel  equal  to  -55  times  that  of  the  water,  it 
will  be 

2-802  x  -55  =  1-54  metres  per  second. 

The  diameter  of  the  wheel  is  of  itself  a  matter  of  indifference ; 
it  should  be  reduced  as  much  as  possible,  so  as  to  lessen  the  cost 
of  construction;  notwithstanding,  it  should  never  be  less  than  twieo 


Ill 


TI1K    l'tt\<    : 


Um  «*><•:.  bright  of  the  fit"  ;    tbua.  in  Uie  prr- 

•hoold  Boll*  Iras  than  4  D 

II  ha.  cftrn  been  asserted  that  the  power  b  Increase 

;  the  rsamrlnr;  it  •.«  iii»  inr  '  that  the 

'  trarsunitti*!  mint  be  b  lb)  fall, 

jl:.1  !•■  8m   ,aa  •.:.  ■  I  ataa  r  .!.-.  .'..-ir.-.  •!.     Il  the  diameter  of  the 
m Wl  k  increased,  the  angular  or  I 

sad,  roasequeolly,  the  momentum  and  actual  force  communicated 
nwh  the  same. 

Taking  the  diameter  at  4  m< 
•  60 

If  a  wheel  uf  this  dinm.  t.  - 
overshot  duct,  with  a 

- 
1  would  not  be  moro 
than 

1-981   x    S5  =  l-Ofl 
and,  consequently,  the  num'.  r  of  bun 
'  60 

par  Bbnta. 

But  then,  as  the  diach  I  ntlet  of 

-J  m.  in  depth  and  1  mi  In-  in  width, 

table,  page  111  |  .al  to 

=  2-7  i   ■ 

Thue,  it  will  be  seen  that  11  M  more 

rapidly  ia  nan-,  arga  of  wufc  r 

by  an  open  outlet,  and  ntly,  leal  costly  in  n 

t  only  gives  out,  at 

•  •ut  by 
may  reach,  a*  ■  :ls  much  as  70 

:  the  wheel,  « 

.  ::li  n:  the  common  under- 

WATtE-WIII.I.Ls    »l: 

389.  Tbcac  wheels  are  fated  wttb 
the  inclination  being  equal  to  a  bane  of  1  Batn  (or  every  1  or  2 
metre*  b  height — daw 
fur  a  short  distance  in  a  circular  channel,  . 
walla. 

!  f..r  low  IUb  of  from  -5  to 

.  .  • 

ppaaJbbi  an^l  tli.it,  nt  r 
part,  it  should  havo  al  or  15  centimi 

fsrilitate  the  dbenga.  action 

is  enlarge tn.  ■-.,„,  |n„ 

line  passing  tl  ■    ,;  n  {\„. 

apace  I- 

•   UM  waler  at 
from  tl  • 

Mo  be  calculated  in  the  aarae  manner 


as  that  :  ■  » ;  as  to  the  diameter,  it  ma 

•In  -. - 1  ■•  r  be  leas  than 

:  ptli  of  lb)  il  -.Hiding 

-    oald  be  i.jnal  to  one- 
fourth  •rnled  by  the  fa 

i.l  be  fr..m  -2  to  -J2  m. :  it  may  bo 
or  ■!'.  in.  for  bib  of  from  1--  to  1-5  m. 

or  float!  are  in  the  f..rm  of  n  cylindrical  curve, 
■  ircular  arr,  tai  .  !iu»  al  the  it, 

and  making  an  angb  ofabool  h  the  stream  ■ 

wn  of  the  wb 

-  i-ireum- 
by  an  angle  of  25",  and  their  thl 

vhen  made  of  WTOUght-irOn  plates,  and  32  to  35  when  of 

wood     The  bottom   of  Ibl  channel  ihoald  have  a  fall  or  in.-liua- 

abont    /.th  ..r  ,  *  -  111 — thai    i-    I  to   that  of  the 

f  a  triangle,  the  base  of  which  il  12  or  l.'i.  and  tlio 

height  1  mcire. 

RW 

390.  Among  the  varieties'  of  turbines  widen  receive  the  action 

of  the  water  throughout  their  whole  circmiitcr.  DBS,  may  be  distin- 
guished those  which  discharge  the  water  al  their  outer  cii 

.1  those  which  allow  il  to  escape  behind.   The  nsefnleflbet 
given  out  by  these  wh  pot  cent,   of  tlie 

••  am  of  water. 
i'..r  these  riont liptionn  ..t'  wheel,  I 
eniated  in  accordance  with  tin 
the  tir^t  kind,  termed  centrifugal  t ur i  ma]  dbmetet  i» 

...1  by  multiplying  the  fourth  or  fifth  of  the  velocity  doe  to 
the  t..t:il  fall  by  7sji  ;  then  dividing  the  quantity  of  water  t..  bt 

discharged  by  Ihe  reenlt  obtained,  and  finally  extracting  the  square 
rool  Of  the  quotient. 

/  nppoas  that  the  mil  b  8*8  m..  and  the  db- 

id.    It  will  l>e  gathered  From 
the  table  on  page  1 11,  that  the  velocity  due  to  the  height, 

,    as  o  57  ill. 
then, 

■  n 

=1642,  and-.      =1314; 


and  further, 


/  80t> 

D^V7854X1G42  =  -787' 


/         800 
D=V785Tx-i 


=  -874  . 


t".r  the  internal  diameter  of  (he  cylindrical  tank  above  the  turbine. 

A.l.l  I  or  So  Ihe  internal  dbmetet  >•(  t! 

which  _■ 

•83  to    !'l  m. 

I  be  equal  to  the  internal  ■  ; 
multiplied  b]  f*S8  "r  I  l.'i.  and  is.  tie  • 

to  1189  m.; 


BOOK   OF   INDUSTRIAL   DESIGN. 


1-137  to  1-319  m. 

When  the  height  of  the  fall  and  the  discharge  of  water  are 
variable,  the  diameters  should  be  calculated  for  the  extreme  cases, 
so  that  the  most  advantageous  proportion  may  be  adopted — that  is, 
the  one  which  will  give  the  best  result  throughout  the  greater  part 
of  the  year. 

If  the  variation  is  very  considerable,  there  should  be  two  or  more 
turbines  employed,  some  calculated  for  the  lowest  discharges,  others 
for  the  mean,  and  others  again  for  the  maximum  discharges. 

The  height  of  the  buckets — that  is  to  say,  the  vertical  distance 
between  the  two  discs  which  form  their  top  and  bottom — is  gene- 
rally about  a  fifth,  or  a  fourth  at  most,  of  the  radius  of  the  interior 
of  the  wheel. 

Tims,  in  the  case  before  us,  the  diameter  being  -787  or  -874,  the 
radius  is  -3985  or  -437,  and,  consequently,  the  height  of  the  buckets 
should  be  -1  to  -11  m. 

The  buckets  being  cylindrical  in  form,  their  entrance  is  normal 
to  the  conducting  channels  which  direct  the  water  against  tliem, 
and  for  these  low  discharges  of  water  should  make  angles  of  68°  to 
70°  with  the  internal  circumference  of  the  wheel — that  is  to  say, 
the  conducting  channels  should  make  angles  of  20°  to  22"  with  the 
circumference.  When  the  discharges  are  large,  this  angle  may  bo 
increased  to  30°  or  45° ;  thus,  for  a  discharge  of  600  to  700  litres 
per  second,  it  is  considered  that  the  angle  should  be  about  30°. 

In  order  to  obtain  the  maximum  useful  effect,  the  velocity  of  the 
wheel  should  be  equal  to  about  -7  times  that  of  the  water;  in  prac- 
tice, one-tenth  may  be  added  to  this  ratio,  or  one-fifth  to  one-sixth, 
without  materially  diminishing  the  useful  effect. 

The  space  between  each  bucket,  taken  at  the  internal  circum- 
ference, should  be  nearly  equal  to  the  distance  between  the  top  and 
bottom  discs  of  the  turbine;  it  should,  however,  never  exceed  18 
to  20  centimetres.  The  internal  and  external  distances  between 
the  buckets  are  necessarily  in  the  ratio  of  the  internal  and  external 
diameters  of  the  wheel. 

In  the  following  table  we  give  the  principal  dimensions,  data,  and 
results  of  several  descriptions  of  turbines,  constructed,  within  the 
last  few  years,  by  MM.  Fourneyron,  Fontaine,  and  Andre  Koechlin. 

These  results  have  been  selected  under  circumstances  where  the 
best  useful  effects  were  given  out : — 

FABLE    OF   DIMENSIONS   AND   PRACTICAL   RESULTS   OF   VARIOUS 
KINDS   OF    TURBINES. 


Total  fall, 

Discharge  per  second, 

External  diameter, 

Depth  of  shrouding, 

Height  of  outlet. 

Number  of  liuckets, 

Numher  of  director  curves 

Number  of  revolutions  per  minute, 

Useful  effect 

Ratio   of   useful  effect  to  absolute 


35  H.  P. 
70°f„ 


100  m 
218  111 
133  m 


2h.  P. 

71°/0 


1-40 

111  10  1 

I  'l in  , 


Data  and  Results. 

Jonval  Turbines,  constructed  by  M 
Andre  KoBChlin,  Mulhouse 

2-720  m. 
684  lit. 
■800  ra. 
•410  m. 

16 
•290  sq.  m. 
•450  sq.  m. 
90  to  158 

13  H.  P. 

2-77  m. 
470  lit. 
■800  m. 
.100  m. 

18 
•220  sq.  III. 

90  to  108 
15  H.  p. 
72°/0 

1-70  m 

•120  m. 

■0706  sq.  in 
2977  sq.  in 
90 
6  H.  p. 

Area  of  escape  outlet  helow  the  wheel,  .  .  . 

Ratio  of  useful  effect  to  absolute  force,  .  .  . 

72°/„ 

REMARKS  ON  MACHINE  TOOLS. 

VELOCITY   OF    THE    TOOL,   OR   OPERATING    PIECE,    IN    MACHINES 
INTENDED    TO   WORK    IN    WOOD    AND    METAL. 

391.  The  principal  machine  tools,  employed  in  machine  shops, 
are — 

1.  The  simple  lathe,  the  self-acting  lathe,  and  the  wheel-cutting 
lathe,  with  adjustable  table. 

2.  Boring  machines  of  various  dimensions,  and  radial  drilling 
machines. 

3.  Horizontal  and  vertical  shaping  machines. 

4.  Planing  machines  with  a  fixed  tool,  or  with  a  moveable  one, 
so  as  to  work  both  ways. 

5.  Mortising  or  slotting  machines,  having  a  vertical  tool  with  a 
revolving  table  below. 

6.  Machines  for  finishing  nuts  and  screws. 

7.  Machines  for  cutting  screws  and  bolts. 

8.  Dividing  engines,  for  dividing  and  cutting  toothed-wheels 
of  all  dimensions. 

9.  Straight  and  curved  shears,  for  shearing  plates. 

10.  Punching  and  riveting  machines. 

11.  Steam  and  other  hammers. 

12.  Straight  and  circular  saws.* 

The  velocity  of  the  cutting  tools,  in  -these  machines,  varies 
according  to  the  nature  of  the  material,  arid  the  quality  of  work 
desired. 

In  general,  for  soft  cast-iron,  it  is  convenient  to  give  a  velocity 
of  seven  to  eight  centimetres  per  second  to  the  tool,  in  sucli  ma- 
chines as  lathes,  and  planing  and  slotting  machines.  This  velocity 
should  be  reduced,  at  least,  to  four  or  five  centimetres  in  shaping, 
drilling,  and  screwing  machines.  When  the  cast-iron  is  hard,  the 
velocity  is  considerably  diminished. 

For  wrought-iron,  the  velocity  may  be  advantageously  increased 
one  half,  because  the  tool  is  kept  well  lubricated  with  oil,  or  with 
soap  and  water ;  thus,  in  turning  or  planing,  the  velocity  may  be 
raised  to  eleven  or  twelve  centimetres ;  and  in  shaping  and  screw- 
ing, to  about  six  centimetres  per  second. 

For  copper,  brass,  and  other  analogous  metals,  with  which  the 
tool  does  not  become  heated  whilst  working,  the  velocity  may  be 
very  much  greater ;  and  for  wood,  its  only  limits  are  those  deter- 
mined by  the  size  of  the  tool,  and  by  the  powers  of  the  machine. 

With  regard  to  the  pressure  and  rate  of  advance  of  the  tool  per 
revolution,  or  per  stroke,  it  necessarily  varies  according  to  the 
dimensions  of  the  machine  itself,  and  also  according  to  the  degree 


nj 


THE    l  DRAUGin 


of  tauh  »*•*  U  to  be  gtreo  to  the  mirfsr. 

&\r  u  murh  nrt»»*o,r>  -snail  lalhr  an  to  that 

apoa  a  krf»  one —  to  a  amatl  drill,  aa  t 

marhioe.     Tbi»  tariai.  fmm  a 

iMth  o/a  BkQlinieUv,  in  aorne  caam,  to  aa  much  aa  i 


\ 

■! — wl»  ii  ii  nvohi-s  and  the 
ttar  wlitn   it   rtv..|\ts.  an  J  thr  cutting 
1  shaping  and  drilling  machines. 


TAR!  TV  AND  PR  M  MTllM)  TOOLS  OR  CI   i 


Tarmibf. 

Drilling  ud  Shapiiuj. 

D   «rr.-,t 

... 

•'■■mied  per  hour 

Numlter 

Wurl  performed  per  hoar 

of  re» 

luii'ini 

wilh 

111111     "      ' 

per   BJlOtll*. 

}  mlmo{  prcMara. 

per  Ullnillr. 

f  */■  of  pretsura. 

CM 

Wrought 

Cut 

Wrought 

Iron. 

Iron. 

rent. 

cent. 

1 

71    i 

ii  i ■<; 

ii  i  •; 

573 

ii  P6 

171  ■;• 

3 

78  i 

7i.  1 

li  1-6 

ii  i ■■; 

171  B 

19-1 

98  7 

.'. 

45-8 

!U-7 

i  .■-:, 

15-3 

99-9 

6 

78  i 

ii  i ■•; 

19-7 

19-1 

673 

8 

1  •  1 

673 

9-S 

113 

49-9 

10 

15-3 

45  8 

7-8 

ii  :. 

99-9 

B4-8 

11 

IS  7 

IS  1 

6-4 

I'M 

38-6 

10 

15  3 

51 

7  0 

lfr9 

39  B 

Willi  1  »;„  „f  pmuura. 

With  1  "i*  '■(  i  -■ 

" 

1 1  r, 

- 

8-8 

B  7 

33-9 

6  1 

46 

97-4 

.VI 

2-fl 

38 

I.VJ 

i  l 

Sfl  1 

9-9 

33     • 

19  8 

313 

1-9 

iiv 

17  1 

:,  i 

]  7 

.'.'. 

10-1 

15-9 

31 

183 

•J7  1 

1-5 

9-1 

i  B 

.94  9 

II 

21 

B  B 

[9-8 

16-9 

13 

i  B 

7-6 

Hi 

1  IT 

-J  11 

11 

l  - 

7-0 

19-6 

11 

n; 

1J1 

18  -3 

I'O 

i  .. 

90 

1   1 

hi 

17  1 

B 

ii 

8-5 

90 

1-7 

I-  i 

lfi-9 

•8 

1  8 

50 

7-6 

Ifi 

9  i 

•8 

11 

1   1 

•j  l 

13-6 

■7 

1-0 

11 

8-9 

i  I 

111 

'ii 

37 

7 

1  1 

1  B 

■8 

>9 

i  i  1 

II 

1  8 

■    ■ 

•8 

B-9 

i  9 

l-,i 

i  :, 

90 

'8 

•8 

i  i 

B  i 

;> 

i 

i  l 

•i 

•7 

I  <> 

•3 

B 

i  B 

■ 

6-4 

•8 

v     1 

•8 

8  .t 

i  B 

•8 

•1 

1  ii 

9-4 

■7 

-1 

•1 

i   • 

1 

■1 

■:i 

I  8 

i  B 

400 

•3 

•5 

-2 

•3 

11 

in 

• 

■  ing  machine  tools  for 
w»  tar.  i  which 

may  be  railed  fur  according  I  ..f  the 

-  .-uti..n.     Thuit,  a  latin-  v/hl  h 
!  10  turn   ar' 


a  diameter,  should  have  a  considerable  rol 
ana  thai  it  t^  ba  chiefly  applied  to  turning  and 
bulky  pieces,  or  snch  as  neasnra  from  ono  to  two  matron  In  dia- 
meter, ahould,  on  ma  contrary,  be  aotnated  by  n  combii 
low,  bat,  at  ii,. 


BOOK  OF   INDUSTRIAL  DESIGN. 


CHAPTER  X. 
THE   STUDY   OF   MACHINERY  AND   SKETCHING. 


VARIOUS  APPLICATIONS  AND  COMBINATIONS. 


392.  Hitherto  we  have  had  to  occupy  ourselves  with  industrial 
drawing,  as  regards  only  the  geometrical  delineation  of  the  princi- 
pal elements  of  machinery  and  architecture.  This  preliminary  study 
being  of  great  importance,  we  have  thought  it  well  to  dwell  more 
particularly  upon  it,  since  also  it  is  the  very  basis  of  all  designing, 
with  a  view  to  actual  construction,  comprehending  not  only  the 
mere  outline  of  objects,  but  also  the  proportions  between  the  vari- 
ous parts,  as  dependent  upon  the  functions  which  each  is  required 
to  perform. 

Machines  are,  indeed,  but  well  calculated  and  thoughtfully  ar- 
ranged combinations  of  these  elements,  and  afford  innumerable 
applications  of  the  rules  and  instructions  laid  down  in  reference  to 
them.  The  study,  therefore,  of  machines  in  their  complete  state, 
naturally  suggests  itself  as  the  next  step  to  be  taken. 

393.  Machines  may,  in  general,  be  classified  under  three  catego- 
ries— machine  tools,  productive  or  manufacturing  machinery,  and 
prime  movers. 

By  machine  tools  are  meant  those  by  the  instrumentality  of 
which  we  work  upon  raw  materials,  as  wood,  metal,  stone  ;  lathes, 
wheel-cutting  machines ;  drilling,  boring,  and  shaping  machines ; 
mortising,  slotting,  planing,  and  grooving  machines ;  riveting  ma- 
chines ;  shears,  saws,  hammers — are  of  this  class.  The  movements 
jf  these  machines  should  be  so  combined,  that  the  tool  or  cutting 
instrument — that  is,  that  part  which  attacks  the  material — should 
move  with  a  velocity  properly  proportioned  to  the  nature  of  the 
work. 

In  the  few  notes  accompanying  our  text  will  be  found  some 
experimental  deductions,  which  may  serve  as  guides  for  adjusting 
the  movements  in  designing  and  constructing  machinery  of  this 
description. 

Amongst  productive  or  manufacturing  machinery,  are  comprised 
spinning,  weaving,  and  printing  machines;  pumps,  presses,  com, 
and  oil  mills ;  and,  finally,  prime  movers  consist  of  those  worked  by 
animals  ;  windmills,  water-wheels,  turbines,  and  steam-engines. 
*  For  the  study  of  complete  machines,  we  have  selected  from  each 
of  these  categories  those  possessing  most  interest  and  generality — 
as  a  drilling  machine,  an  instrument  so  very  useful  and  so  much 
employed  in  machine-shops  and  railway  works;  a  pump  for  raisino- 
water,  serving  for  domestic  purposes  as  well  as  for  important  manu- 
facturing establishments;  two  examples  of  water-wheels,  showing 
various  arrangements  and  forms  of  floats  or  buckets ;  a  high  pres- 
sure expansive  steajn-engine,  with  geometrical  diagrams,  determin- 
ing the  relative  positions  of  the  principal  pieces  in  various  circum- 
stances ;  and,  finally,  a  set  of  belt-driven  flour  mills,  constructed  on 
a  system  recently  adopted. 

Before  proceeding  to  the  description  of  these  machines,  it  will 
be  necessary  to  habituate  the  student  to  draw  from  the  reality, 
for  up  to  the  present  time  he  will  have  done  nothing  but  copy 
the  various  graphic  examples  to  this  or  that  scale.  The  operation 
iu  question  consists  .in  drawing  with  the  hand,  the  elevation,  plan, 


sections,  and  details  of  a  machine,  preserving,  as  much  as  possible, 
the  forms  and  proportions  of  each  part ;  and  then  taking  the  actual 
measurement  of  each  part,  and  laying  it  down  in  figures  in  its  par- 
ticular position  upon  the  drawing :  this  duplex  operation  of  sketch- 
ing and  measuring  constitutes  the  study  of  the  rough  draughting 
of  machinery. 


THE   SKETCHING   OF  MACHINERY. 

PLATES  XXXV.  AND  XXXVI. 

394.  Before  commencing  the  sketch  or  rough  draught  of  a 
machine,  it  is  absolutely  necessary  to  look  carefully  into  its  organi- 
zation, the  action  of  the  various  working  parts,  the  motion  of  the 
intermediate  mechanical  connections,  and  finally,  its  object  and 
results.  The  object  of  this  preliminary  examination  is  to  give  the 
draughtsman  a  good  general  idea  of  the  more  important  parts — 
those  which  he  will  have  to  render  most  prominent  and  detailed 
when  he  comes  to  make  a  complete. drawing  of  the  whole;  such 
drawing  comprising  a  series  of  combined  views,  together  with  sepa- 
rate diagrams  of  such  details  as  may  not  be  apparent  in  the  former, 
or  require  to  be  drawn  to  a  different  scale  to  render  them  intelligi- 
ble. In  fact,  this  must  be  done  in  such  a  manner,  that,  with  tho 
aid  of  the  sketch,  a  perfect  representation  of  the  machine  may  be 
got  up,  which,  if  necessary,  may  serve  in  the  construction  of  other 
similar  machines. 


DRILLING    MACHINE. 
PLATE    XXXV. 

395.  In  order  to  give  an  exact  idea  of  tho  manner  of  sketching 
machinery,  we  take  a  simple  machine  as  an  example ;  this  we  sup- 
pose to  be  represented  in  perspective*  in  fig.  ^\,  this  view  being 
instead  of  the  machine  itself. 

This  machine  is  for  chilling  metals :  it  consists  of  a  vertical  cast- 
iron  column,  A,  which  forms  part  of  the  building  or  workshop. 
This  column  is  hollow,  and  rests  by  an  enlarged  base  upon  a  stono 
plinth,  e,  imbedded  in  the  ground,  and  at  its  upper  end  it  supports 
the  beam,  c. 

Upon  one  side  of  this  column  is  cast  the  vertical  face,  D,  which 
is  planed  to  receive  three  cast-iron  brackets,  e,  f,  g,  attached  to 
it  by  bolt9.  To  the  opposite  side,  d',  of  the  same  column,  is  in 
like  manner  attached  the  bracket,  H,  which,  witli  the  middle  one, 
F,  on  the  other  side,  serves  to  carry  the  horizontal  spindle,  r. 
This  spindle  carries  on  one  side  the  cone-pulley,  J,  over  which 
passes  the  driving-belt,  K,  and  on  the  other  extremity  it  has 
keyed  upon  it  the  bevil-pinion,  l,  which  gears  with  a  larger 
bevil-wheel,  M.     This   last  is   attached   to    the   vertical  shaft,  N, 

*  In  a  subsequent  chapter,  we  shall  explain  the  general  principles  of  par&lleJ  %al 
exact  perspective. 


I.lt\l  ..III 


'•JU,.4.i.f.  and  i.  BMrreahle  in  the  brark-l- 
keaifcyi    r  aad  o.     TV.  •haft  rmimi  duple*  moirrrwii' 
<•    -.:.:. u    ...    r    •_         .   ■>        ■     •    i  .  -re  ..r  !.■«   rapid,  »••■■  ■r.l.r,.-  ».   if- 
Wl,  K,  i.  .*  IS*  U-a»  or  greater  dkueotor  of  lb*  cone-pulley ;  and 
Um  other  mtirai  and  rectilinear,  due  to  lh«  acUon  pi 
whira  Work*  la  aa  interna]  arrew  In  the  cod  of  the  In 
That  arrrw  earrie*  at  iu  upper  rod  a 

■mail  pWoa,  o>  the  abaft,  «,  of  »h.h  i.  prolonged  downwarda,  and 
terminate*  in  a  amall  hand-wheel,  a. 

To*  object  to  be  drill. ,1  U  I  pair  of  jaWB, 

'•a  groove*  upon  the  table,  T,  and  capable  of  adjustment  bock  and 
!bnrard  by  meana  of  the  arrew,  A,  t 

aaodJ*.     The  table,  T,  i«  made  in  two  piece*,  »o  aa  to  f-nii  a  collar 
a>-  ut  the  rolumn,  A,  and  il  ia  bad  at  any  I  hi  upon 

thk  colanin  by  aeana  of  the  praaauro  nh  \\,  r,  i  i  ■■  i 
of  the  table  from  the  drill,  J.  ■ 

pinioo  on  the  abaft,  a,  ■ 

•station  of  thia  handle  and  Um  pinion  neceiwarily  et 

or  drarenl  of  ibe  tafah. 

TV  drilling  machine,  then,  fulfil-  the  folk  na  :  on 

ibe  one  hand,  the  drill,  J,  ia  worked  at  a  gn 
■ 

with  tin1  nature  of  tho  maleri 
upon;  .i  •  r  luuul,  the  lalile  Which  BUTi 

I  ia  .a|al.!e   oi 
nwlpg  to  the  foraw  and  din  -  whilst  it  may 

alao  be  net  eccentrically,  when  ncccaaary,  by  turning  it  lo  the  le- 
imn. 

anatraction  and  action 
dI  tin-  machine,  tho  .1; 
man  rur.  H 

■ 
I'ifoaa. 

Irical  elevation 

iimn,  a,  with  ■  and  the  lablo, 

I 

iiraii_-ht.au  well  aa  in   I  with  it  without  the 

aaaiatatx  a  of  a  rata,  I  .  thus, 

•  Um  ooJnmn,  a,  draw 
nr ;  then  draw 
parallel  I  ..f  lha  drill-etock,  > ;  than  the  hori- 

zontal, '.  -I  tin'  bartt-wbeel,  i.. 

and  tb< 
•  p,  o  » 

o;   Anally,   dr..  i  I  /  nu<l  I  i, 

of  Uw  bracket,  it ;  an 

the  bnttum  am)   top  of  tin-  BohUDB.     At  thin   atagt 
aary    ktl   lay   down    tlie  meaeuretnent*    opon    the 
column  principal  |«rt»  of  thi 

.ml  upon  it  for  the 

height    to   be   meaaur. 

' 


:•  nt  at  the  baaa 
and  aui 

•  it  tliat   they  • 

.  the   aini.uiit   ..f  i'|«  ning  U  in;;  t!.. 
rule,  and  w  ritti  n  down  upon  I 
ra  may  l«-  oh 
rule,  to  the  eb  -  alwaya 

ter,  when  it  ii 
obtain  thi  r  baaa.     In  thk 

ii  nccesaary,  aa  haa  I- 
i.  bj  I  [416. 
To  obtain  Ua  utra  lluo 

■iliimn,  place  toe  extremity  of  Um  rule  at  ?,  agalnat  tlio 
oolnmn,  and  lit  it  Bi  i,  of  1 1 1«* 

«|nir.«'  '1   tin   riilr  will 

b«   that  nf  t'  i,  tn    which   moat    lie   addi-d    Uu'    radium   i   i"1,  uf  the 
column. 
If  the  centre,  i,  wara  not  approachabla  with  Um  i 

Um  Interna]  dietanea  between.  Hw  nrfiei 
column  nnd  that  of  tin-  acrow,  and  (hen  add  the 
of   tin'    BCrOW   and    column.     Whan    tin  H 

than  the  length  of  the  meaarxring-nile,  a  rod  or  tape  moat  I«j 
I.      When,    Indeed,    the    ■: 

•  iint   of  skill,   h"  may   take   t  ant,   i  i*, 

directly,  by  applying  the  rule   opon  lha  -  column 

Um  avis  of  Uu 
in  aneh  I  manner  that  the  rule  ihall  to  the  column, 

«li.  ii  tl.  en  Um  two  pointa  wU  bo  Um  meaanroment 

■ 
■  m   horizontal  linea,  at  n,  o  ;■.  o  f,  »  L 
The  moaaaramenti  indlcatod  opon  I  ••  bow  all  thaai 

are  obtained. 
'I'll.  |.i.  ■  •  ding  operationj  will  allow 

laying  off  the  relaUn  Um  main  |«rt« 

which  go  t tnpoat  Um  machine  to  be  akotrhed.    We  have  nest 

•  ll!  the  iniii'.r 

of  the  machine.    To  t li i~,  effect,  and  t.i  avoid  eonfoston,  it  >- 

diffbront 
f  ili.  in,  opon  «liiili  Um  dim.  n 
properly  bjdk 

I  •  nt,  in  eleradon  and  plan,  the    detail   of  tlia 

1'i.uki  i,  i,  which  npporta  Um  >liati-.  i  and  >,  with  Um 

beril-wbi  >  Umm  rlowi  are  not  lurBcienl  t" 

..I  the  dlmenaloni  of  tlii-  braefcel ;  thm  it 

* 

I — \i,  nnd    projl  '  l.'nn  ..I   the 

•  r  .  ii  !■•  Ilka* 

I  Um  tr**fng1 '-',  which  Inil'l-  up  the  abaft,  ••,  t"  Um 

Il   at    the    line, 

■how  the  braaas*    which   ■  >amal  of  tho 

■ 
a  larger  ecolc.  ao  aa  to  indk  and  to 


BOOK   OF    INDUSTRIAL   DESIGN. 


give  room  for  the  measurements ;  and  it  may  be  observed,  that,  for 
a  draughtsman  who  has  not  much  practical  knowledge  of  machine- 
ry details,  it  will  be  necessary  to  take  down  or  separate  various 
parts,  such  as  the  cap  and  the  upper  brass.  With  regard  to  wheel- 
work,  it  will  be  sufficient  to  give  the  section  of  the  web  and  boss, 
as  indicated  in  figs.  2  and  7,  and  a  section,  as  tig.  S,  of  one  of  the 
arms  when  the  wheel  has  any,  and  then  the  numbers  of  teeth  and 
arms  must  be  counted  and  set  down. 

When  all  the  parts  of  any  detail  are  thus  sketched  out  in 
elevation,  plan,  or  section,  the  draughtsman  must  take  the 
measurements  of  each,  and  set  them  down  in  their  appropriate 
positions  upon  the  sketches,  as  indicated  in  the  figures ;  being 
mindful  to  see  that  the  principal  measurements  coincide  with  those 
laid  oft'  in  the  complete  general  view  already  commenced.  The 
measurements  of  the  diameter  of  the  pitch-circle,  and  of  the  width 
of  the  teeth,  will  be  sufficient,  in  addition  to  what  has  already 
been  directed  to  be  done  in  reference  to  wheel-work,  the  proper 
ratios  being  maintained  between  those  in  gear  with  each  other. 
As  many  parts  of  machinery  require  to  be  in  proportion  to 
each  other,  a  knowledge  of  such  relations  will  enable  the 
draughtsman  to  dispense  with  a  great  deal  of  tedious  measuring 
and  sketching,  as  in  the  case  just  alluded  to,  of  wheels  working 
together. 

The  remaining  parts  of  the  machine  are  to  be  detailed  in  the 
same  manner.  Thus,  figs.  9,  10,  and  11,  represent  a  vertical  sec- 
tion, a  plan,  and  a  side  view  of  a  portion  of  the  table,  T,  with  its 
holding-jaws,  and  its  elevating  pinion  and  shaft.  Fig.  1:2  is  a  ver- 
tical section  of  the  lower  extremity  of  the  drill-stock,  or  spindle,  n, 
with  the  drill,  d,  in  elevation.  Fig.  13  is  *a  section  of  the  cone- 
pulley,  J.  Figs.  14  and  15  show,  in  vertical  and  horizontal  section, 
the  mauner  of  jointing  the  screw,  o,  into  the  upper  end  of  the 
spindle,  n.  Finally,  figs.  16  and  17  give*  complete  detail  of  the 
mechanism  for  elevating  the  table,  T,  as  well  as  that  for  fixing  or 
adjusting  it  at  any  required  height. 

397.  On  all  the  preceding  details,  we  have  quoted  the  measure- 
ments of  the  different  parts  exactly  as  they  should  be  upon  an 
actual  machine.  These  measurements  are  expressed  in  millimetres, 
as  in  former  examples,  this  measuring  unit  being  adopted  because 
its  minute  scale  renders  fractions  unnecessary.  We  have  also 
slightly  shaded  various  parts,  as  is  generally  done  where  the  com- 
plication and  variety  of  forms  would  otherwise  lead  to  confusion 
and  error.  Besides,  in  this  manner,  a  few  touches  of  the  pencil 
show  at  once  whether  this  or  that  portion  is  round  or  square,  and, 
in  many  instances,  the  labour  of  drawing  additional  views  will 
thereby  be  dispensed  with. 

In  order  to  facilitate  the  proceedings  of  beginners  in  sketching, 
we  would  recommend  them  to  delineate  the  main  centre  lines  with 
the  aid  of  a  rule,  and  the  circles  with  compasses,  though  the  dimen- 
sions of  the  latter  need  not  be  exact.  This  will  give  the  sketch  a 
much  neater  appearance,  and  render  the  various  objects  or  details 
more  regular.  It  is  with  this  view  that  sketchers  frequently  employ 
cross-ruled  paper,  with  horizontal  and  vertical  lines  equally  spaced. 
That  portion  of  Plate  XXXV.,  upon  which  are  sketched  figs.  9,  10, 
and  11,  is  of  this  description. 

It  will  be  understood,  that,  if  the  lines  ruled  upon  the  paper  are 
at  equal  distances  apart,  corresponding  to  one  or  more  units  of  the 


scale  to  which  the  sketches  are  being  nride,  these  may  be  drawn  in 
correct  proportions  at  once,  in  which  case  it  will  be  unnecessary  to 
write  on  the  various  measurements. 

The  example  which  we  have  given  as  an  introduction  to  the 
study  of  sketching  machines,  will  have  somewhat  familiarized  the 
stu  lent  with  his  operations  even  now.  The  applications  contained 
in  the  subsequent  examples  will  suffice  to  complete  this  study, 
which  is  one  of  great  importance  to  the  draughtsman  and  construct- 
ive engineer. 


MOTIVE    MACHINES. 


WATER-WHEELS. 


PLATE     XXXVI. 

398.  The  water-wheel,  represented  in  fig.  1,  has  plane  floats,  and 
works,  through  a  portion  of  its  circumference,  in  a  concentric  cir- 
cular channel.  It  receives  the  water  from  over  a  sluice-gate,  a 
little  below  its  centre,  and  is  of  the  undershot  description. 

The  wheel  is  composed  of  several  parallel  shroudings,  A,  in 
which  are  fitted  the  radial  wooden  bearers,  B,  carrying  the  floats,  c. 
When  the  shroudings  are  of  east-iron,  as  is  supposed  in  the  present 
example,  they  are  cast  in  one  piece  with  the  arms,  D,  and  central 
boss,  E,  and  are  firmly  secured  by  keys,  a,  upon  the  shaft,  F,  also 
of  cast-iron. 

The  head  of  the  channel,  G,  which  embraces  the  lower  part  of 
the  wheel,  is  constructed  with  a  piece,  h,  in  cast-iron,  called  tin? 
neck-piece,  which  is  fitted  upon  the  cross  timber,  i,  and  let  into  the 
two  lateral  walls.  Against  this  neck-piece  works  the  wooden 
sluice,  J,  above  which  overflows  a  certain  depth  of  water,  falling, 
in  succession,  upon  each  float  of  the  wheel  as  it  comes  round, 
causing  it  to  turn  in  the  direction  of  the  arrow.  The  rotatory 
movement  of  this  water-wheel  is  taken  off  by  the  cast-iron  spur- 
wheel,  K,  mounted  upon  the  end  of  the  shaft,  F,  and  gearing  with 
the  east-iron  pinion,  L,  the  shaft  of  which  communicates  with  the 
machinery  to  be  set  in  motion. 

In  giving  this  example,  our  object  has  been  to  examine  this  motor, 
not  only  with  reference  to  its  accurate  delineation,  but  also  with  a 
view  to  sketching  similar  wheels,  as  well  as  to  constructing  and 
setting  them  up,  with  their  channel  and  sluice  gear. 

THE    CONSTRUCTION   AND   SETTING   UP*  OF    THE    WATER-WHEEL. 

399.  The  channel,  G,is  built  up  of  hewn  stones,  the  lateral  joints 
of  which  converge  towards  the  centre,  o,  of  the  wheel,  and  they  are 
imbedded  upon  a  foundation  of  ordinary  stone-work.  All  thu 
masonry  is  put  together  with  mortar,  made  with  hydraulic  lime, 
the  joints  being  finished  with  Roman  cement.  In  some  localities 
the  channel  is  of  bricks  or  freestone,  and  sometimes  even  of 'wood. 
The  apparent  concave  surface  of  the  channel  should  be  perfectly 
cylindrical,  and  concentric  with  the  external  circumference  of  the 
wheel.  Also,  before  placing  the  latter  in  its  proper  position,  this 
surface  should  be  finished,  and  rendered  quite  smooth  and  true, 
which  may  be  done  with  the  assistance  of  a  temporary  shaft,  o. 
with  the  actual  shaft  of  the  wheel,  in  the  following  manner: — 

The  shaft,  F  (146),  is  adjusted  to  the  exaet  height  at  which  it  is 
to  be  afterwards,  and  it  is  made  capable  of  rotation  in  appro 


Till:    1 


.■   ■      :     ■     .. 

::...  shaft  are  fitted  tbe  shrnMingi,  A.  each  connected  to 
i  .  tbe  outside  of  Um  anna  are  then 
tsaapsraray  attached  two  ladaal  pieces  of  wood,  baring  a  cross  piece 
:  to  Ihs^  the  c*ler  edge  rfw1sk*Ue*ade  true  aiid  parallel 
,'jft.  sad  rotarsirot  with  tbe  external  edges  of  the  c 
at  that,  if  the  abaft  i»  now  made  to  I 
v    1  describe   a  cylindrical   surface,  ■ 
precisely   that   which  the  ehaaoel  should   posse*. 
therefore,  as  so  accurate  guide  in  giving  the  channel  its  appropriate 
.     •  h    .r 

Tbe  lower  part  of  the  channel  U  continued  on  in  a  straight  line, 
i  waliiaii ilSJ  at  the  vertical,  o  4,  and  in  a  din%-li<>n.  b  r.  - 
iodiaed  to  a  short  distance  away  from  the   ■  tato  the 

escape  of  the  water. 

The  cross  timber,  t,  which  surmounts  tbe  masonry  of  the  ch.in- 
d<  I.  and  which  recedes  the  ae 

he  channel,  so  as  to  allow  the  sluice-gate  to  be 
broaght  closer  up  to  tbe  wheel.     The  neck-piece,  a,  which  forma 
the  crest  of  the  channeljis  more  frequently  constru.: 
than  of  either  wood  or  atone,  as  that  material  does  not  require  to 
be  so  thick,  for  resisting  the  pitas  un  of  tbe  - 
neck-piece  is  at  a  distance   below  the  Bpp 
• 

I 
i  imsiifa  rilily.  according  to  the  quantity 
and  the  width  I 

neck-piece,  a  ea  Bed  in  the  ma- 

■ 

IS    .      ...  so  that  it  may   n.-l   ':- 
ii.i-  smalt  raw  . 
this,  again,  ser-  iting  bodies,  as  tree*.  •'■ 

ently  of  a  grating  placed  further  behind,  and  prat 
1  injuring  the  wheel. 
Tbe  sluice  eonsista  of  two  strong  oaken  planks,  haring 
and  toagaed  jointa,  and  being  made  thicker  at  the  middle  than  at 
tbe  extremities,  where  the  wheel  is  of  a  greater  width  than   1 , 
metre.    The  amount  of  inclt: 
by  drawing  a  perpendicular  to  tlw-  • 

drawn  near  the  middle,  or,  perhaps,  I  i  of  the 

'Hie  sluice  i«   I 

rml  wall*. 
At  the  upper  parta  of  these  an 

•  cast-iron  re- 
attached to  tbe  two  side-posta,  a.     These  racks  r>  - 

.  which  also  guide  them,  and,  on  the 
- 
tal  axi- 

wheel,  q,  actuated  b]  a,  which  ma;, 

plan—re  from  ah, it e— a  winrh-handle,  or  hand-mi 
uf»-n  aba  appar  •  rtmnity  of  its  wrlir.il   spindle  f^r  thin  purpose. 

•luire,  and.  eonaeqoi  I 

with  the  greatest  nicety,  as  well  aa  of  the  total  shutting  ofT  of  the 

»»••  r  (r  m  th<-  wheel. 


The  shroudi:  j 

panes!  in  it,  as  at  s,  i.  shown  in  the 

r  ends,  of  the 
...  to  which  the  tl  at*  are  boll 

'  •  -  ■ 

«   only  the  case  when  the  discharge,  and 
rj  small, 
the  can 

- 
C  and  i.'. 

in  the  U|  1       In   both 

thecarri-  - 

rder  to  facilitate  the  adjust- 

them  in: 

retains:  N 

. 

.-•>  are  of  wo.-  necessarily  be 

-.  as  shown  in  figs.  5  and  ti ; 

. 

-  can  at  all  timi  - 
should  they  begin  I 

are  adjust 

I 
shroudi:  .  iron  straps,  as 

-   and  are 
■  nans  of  last  b 
1   fn>m  the  h 

I  are  nailed  down  upon   : 
bastsgal 

n  of  the 
rataav     II 

■  ' 

h  ■   .- 
arfgh   „  and  channel 

•  -    -  '  -    '  :'  *■*■     Tbe 

I 

•pace  in 


BOOK   OF   INDUSTRIAL   DESIGN. 


lines  passing  through  the  centre,  and  representing  the  sides  of  the 
carrier-pieces  upon  which  each  float  is  placed.  Two  circles  must 
next  be  described,  expressing  the  depth  of  the  shrouding.  Then 
the  complete  outline  of  one  of  tho  carrier-pieces  must  be  drawn, 
with  the  dimensions  quoted  on  the  figure ;  and  the  key  and  bolts 
may  also  be  indicated  upon  it.  Afterwards,  to  complete  the 
drawing,  it  will  be  sufficient  to  describe  a  series  of  circles,  passing 
through  the  bolts,  the  ends  of  the  floats  and  carrier-pieces  of  the 
key.  and  of  the  counter-float.  With  regard  to  the  floats,  and  to 
the  arms  of  the  shrouding,  as  well  as  to  the  spur-gear  for  trans- 
mitting the  motion,  the  student  may  refer  back  to  the  diagrams 
and  explanations  already  given  concerning  similar  objects.  The 
same  remark  applies  to  the  lifting  apparatus  of  the  sluice-gate, 
which  is  also  composed  of  gearing  already  treated  of  in  the  course 
of  the  studies. 

DESIGN   FOR    A   WATER-WHEEL. 

401.  If  it  is  in  contemplation  to  make  a  design  for  the  con- 
struction of  a  water-wheel,  analogous,  we  shall  suppose,  to  the  one 
above  described,  it  is  simply  necessary  to  ascertain  the  height  of 
fall,  and  the  amount  of  discharge  per  second,  of  the  water  at  our 
disposal,  and  to  refer  to  the  calculations  and  practical  rules  which 
accompany  our  text,  to  be  able  to  determine,  on  the  one  hand,  the 
diameter  and  width  of  the  wheel,  and,  on  the  other,  the  depth  and 
interstices  of  the  floats,  and  their  number.  By  referring  back,  also, 
to  the  tables  and  notes  relating  to  the  resistance  of  materials 
(Chapter  III.),  we  shall  be  able  to  complete  the  remaining  dimen- 
sions for  the  shaft  and  its  journals,  the  shrouding  and  its  arms. 

The  study  of  water-wheels  of  this  description  will  be  much  sim- 
plified, if  we  consider  that  certain  dimensions,  such  as  the  thickness 
of  the  floats,  the  section  of  the  carrier-pieces  and  shrouding,  and 
the  diameter  of  the  bolts,  as  well  as  the  details  of  the  sluice  appa- 
ratus, do  not  sensibly  vary;  and  for  them  the  draughtsman  may 
refer  entirely  to  those  indicated  upon  the  drawing,  which  are 
themselves  examples  of  actual  construction. 

SKETCH   OF   A   WATER-WHEEL. 

402.  The  sketch  of  a  water-wheel,  already  constructed  and  set 
up,  is  a  very  simple  matter;  for  the  apparatus  consists  of  a  repeti- 
tion of  various  pieces,  and  it  is  sufficient  to  obtain  the  measure- 
ments of  one  only  of  each  kind.  Thus,  after  having  measured  the 
diameter  and  extreme  width  of  the  wheel  wilh  the  aid  of  a  long 
rule  or  tape,  and  counted  the  number  of  buckets  or  floats,  of  the 
shroudings,  and  of  the  arms,  we  have  merely  to  take  the  sketch  of 
a  single  float,  with  its  carrier-piece  and  accompaniments,  then  to 
make  a  section  of  one  of  the  shroudings,  another  of  one  of  the 
arms,  and,  finally,  a  third  of  the  boss  and  shaft. 

The  details  given  in  figs.  2  to  10  show  the  various  parts  of 
which  the  sketches  have  to  be  made,  as  detached,  together  with. the 
corresponding  measurements.  Fig.  20  is  a  transverse  section  of 
one  of  the  arms,  d,  of  cast-iron,  taken  near  the  boss. 

The  sketching  of  the  sluice  apparatus  consists  in  making  a 
section  of  the  side-posts,  with  their  cap-piece,  and  of  the  sluice 
itself;  then  a  detailed  view  of  one  of  the  racks,  with  its  pinion 
and  friction-pulley,  and  of  the  worm-wheel  and  worm.  As  to  the 
amount  of  inclbation  of  the  sluice  and  side-posts,  it  has  already 


been  seen  that  it  is  determined  by  a  perpendicular  to  the  radius, 
entering  near  the  middle  of  the  depth  of  water  at  the  outlet,  at 
the  circumference  of  the  wheel.  It  may,  however,  be  found  by 
means  of  a  plumb-line,  let  fall  from  one  of  the  edges  of  the  cap- 
piece  down  to  the  level  of  the  water,  by  measuring  the  horizontal 
distance,  r  s,  of  the  plumb-line,  from  one  of  the  sides  of  the  side- 
post,  and  then  the  vertical  height,  r  I.  By  applying  a  rule  against 
the  side-post,  and  down  to  the  neck-piece.  H,  we  can  always  obtain 
the  actual  distance  of  the  top  of  the  latter,  either  from  the  pro- 
longation of  the  horizontal,  r  s,  «r  from  the  cap-piece,  P.  of  the 
sluice.  To  obtain  the  horizontal  distance,  r  s,  with  exactitude,  it 
should  generally  be  taken  at  a  given  distance  above  the  level  of 
the  water,  and  chalked  upon  one  of  the  side-walls  of  the  channel ; 
it  is  also  advisable  to  make  use  of  a  spirit-level.     (Plate  I.) 

In  order  to  take  an  accurate  sketch  of  the  neck-piece  and  the 
channel,  it  is  almost  always  necessary  to  stop  the  water  behind 
by  means  of  a  dam,  so  that  the  parts  requiring  to  be  examined 
may  be  dry  and  open.  The  sluice  must  also  be  taken  away,  as 
well  as  a  few  of  the  floats  of  the  wiieel.  We  may  remark,  that 
this  labour  may  be  avoided,  when  it  is  known  that  the'  height  and 
thickness  of  the  neck-piece  are  nearly  always  equal  to  those  indi- 
cated in  fig.  11;  and  as  to  the  arrangement  of  the  masonry  or 
brickwork,  of  which  the  channel  may  be  constructed,  it  will  be 
recollected  that  all  the  lateral  joints  are  pointed  towards  the  centra 
of  the  wheel. 


OVERSHOT  WATER-WHEEL. 

Figure  12. 

construction  of  the  wheel,  and  its  sluice  apparatus. 

403.  Overshot  water-wheels,  with  buckets,  receive  the  water 
from  a  duct  placed  immediately  above  them,  and  allow  it  to  escape 
from  as  low  a  part  only  as  possible.  They  are  constructed  of 
wood,  or  of  cast-iron.  In  the  first  ease,  which  is  the  simpler  and 
more  economical,  the  shaft,  the  arms,  and  the  shroudings  are  of 
oak.  The  lower  part  of  the  wheel,  represented  in  the  drawing, 
fig.  12,  is  of  this  description.  The  buckets  and  the  inner-rim  are 
likewise  of  oak,  or  of  iron  plates.  As  this  wheel  is  of  small  dia- 
meter, its  shaft,  f,  has  only  six  sides ;  and  consequently,  each 
shrouding,  A,  of  the  wheel  has  only  six  aims,  d,  which  are  recessed 
into,  and  bolted  upon,  a  central  cast-iron  frame,  e,  which  is  itself 
keyed  upon  the  shaft.  The  transverse  section,  fig.  13,  shows  the 
manner  in  which  the  arms  are  attached  to  this  frame.  The  wooden 
shroudings,  A,  are  generally  composed  of  two  rings,  placed  one  on 
the  other  in  such  a  manner  that  the  joints  of  each  are  opposite  to 
solid  portions  of  the  other,  to  "break  bond,"  and  obviate  tie  ten- 
dency to  warp.  A  portion  of  the  shrouding  is  represented  as  de- 
tached in  figs.  14  and  15.  These  rings  are  held  together  by  screw  s, 
v,  or  by  nails  or  pegs ;  and  at  their  junction  with  the  arms,  a  couple 
of  bolts  are  passed  through  all,  as  indicated  in  the  transverse  sec- 
tion, fig.  16.  The  buckets,  c,  are  either  let  into  grooves  of  smai. 
depth,  upon  the  inner  face  of  the  shrouding,  as  seen  at  c',  in  figs.  14 
and  15,  or  they  are  retained  by  bracket-pieces,  c:  and.  added  to  ties, 
strong  tension-rods,  b,  hold  the  whole  together,  being  secured  to 


Ot»  *ft>«tta~«,  A.  as  cither  side  of  the  borkeU.     These  tco.ion- 

rods  Sfs  ftlrd,  ■  hcB  the  inner  nui.  «. . .r  I- •  ! t-tu  of  the  bu. 

btaa  Mil. J  or  •rresrrd  to  tbo  inn.  r  edges  of  Ute  »hr..udi n g«.    The 

■tan pilot!  are  further  •treogthrned  externally  by  a  n: 

trap.  n.    klfir  V  the  f.  ll.-e  ..fan  ordinary  wheel,  and  c- 

tbo  c«ou  of  the  .lu;  J.»  «hr..oding. 

Bonntim—  the  backets  ar.    partly,  of  wood,  and  parti) 
p'atr.  to  giro  th.  m  greater  «!r.  ngth.     11m-  edfi  - 
•  bo  defended  with  metal,  aa  they  an 

the  wheel  i»  of  cast-  r.  at  dia- 

meter, bat  of  the  size  represented  in  tin-  u]  l_'.  I  lie 

anna  and  the  boa*,  f,  may  !■■ 

. 
»',  ai.-i  ilxjut  Jth  inch  in  thick- 

ness.    To  arrorc  th' 

-.  tn  which  Ihey 
the  wheel,  the  buckets 

it  i,  or  arc  ti\<  : 
by  amall  acrew-bulta,  i',  figs.  17  a! 
Tbo  advantage  of  1n.1l.l11/  0 

rm,  which  enlai 
capacity,  and . 

whilst  the  ww  »ni  i—i lily  eooaial  of  two  rectilinear 

re  of  tlir  wheal, 

Tne  a  -1.  n  channel,  m,  to  the  top  of 

-.  moving  in  aide 

if  virtual  racks,  o,  and 

nies  the  winch-handle.  Q.   The 

fond  the 

actual  .urunii:  oold  lie  a 

■  ■I  the  wheel,  with  the 
r  into  tin'  I'n 
splashing  and  loM  "f  water  by  allowing  the  air  to 
escape  bit,  rally.    The  depth  of  the  outflow  of  water  •!• ; 
the  distance  ot  ttom  of 

the  channel,  and  should  alw . 

existing  betwi  ■  la.    The  |  ,.|  ii„. 

Ihe  wheel  in  the 
■i  .if  the  arrow,  and  II  by  an  intcrn.'ill v- 

I'-UllillgK. 

Thi»  •  the  drawing  ii  simply  tndioated  by  its  pitch 

•   i'.ar»  »iili  ill.  pinion,  i.,  mounted  on  th.-  ■ 

with  the  machinery  in  the  i. 

H'T    WATER- 

rincipal   parts  of  an  ■  ■ 

way  aa  thai  nf  tin. 

tl  al  when  (In  at 


- 

an  angle 

mity,  aa 

• 

ntiMir  ia  a  ciiiilinui'ii-  may  be 

■    IS,  17, 
and  18. 

-    tching  this  wl  i  n  in  tin-  pn 

case  may  be  lik 

-  and  taking  an  accurate  sketch  of  one  of  them,  l< 
with  tin-  accompanying  mcasurcim  ■  •  - 

mal  and  external  diameters  of  the  shroudings;  tlun  the 

depth  from  t  tn  ■/,  Bg.  17.    Finally,  if  it  ia  itain  iho 

'in  or  curvature  of  the  bucket,  it  will  In.  iieoeaaarj 
one  down,  and  I  pattern  of  it,  by  app 

■ 
t'.ir  the  forma  of  a  beaJ-b  eta,  .  a  bJefa  are  difficult  to 

Aa  i"  the  sketch  of  the  oi 

as  the  boas,  the  arm*,  and  also  the  sluice  a|  i  uliarity 

ordiflionlty  can  present  itaelf  which  need  detain  aa  lure.    Tim 
drawing,  moreover,  indicates  all    It  trementa 

which  are  nocoaoiry. 
In  designing  an  overshot  water-wheel  il  to  know 

hi  of  fall,  and  the  daily  discbarge  of  the  water.    With 
■  these  partienlara,  we  must  sm.j  Ij  refer  to  irfh- . 
..id  Practical  I1 


W  ,\T  E  R-PUM  PS. 
PLATH   XXXVII. 

GEOMETRICAL     StllHlTlnX. 

405.  We  have  already  indicated,  i; 
tin ii-,  the  \ari"  M  '  mips,  with  their  proper  dimi 

in  proportion  t..  the  quantitioa  of  water  to  be  Furnished  by  them. 
We  new  propone  t"  enter  npon  mori 

;lnir  eonstroction, actton, and  performance, 
I'ur  this  purpi.se  we  mbined 

lifting  and  forcing  pump,  the  discbarge  of  wl  1 1  ■  •utiriu- 

i.ns,  although  it-  Bonatruction 

I    imp. 

I,  on  Plata  \ XX VII.,  repreaenta  a  n 

taken  throngfa  the  axia'of  this  pump.    I; 

cylinder,  a,  tamed  out  fur  the  greater  |»>rti..n  ••!     • 

• 
or  lift-pipe,  c,  below.    Thin  lwise  is  bolted  down  either  i 

liml..  r-.  0,  ..r  to  I   stonework 

r  frame,  dividi 
partition,  at,  and  having  the  aidaa  formed  •  Iwoia- 

npOO   which  the  hra-s  .  D    shut. 

The  pip  below  in  a  i!  -  of  which  the 

iuction-fj  ed,  extending  down  to  the  water  to 

Towarda  the  nppat  sujnp  eyhndar,  i 


BOOK   OF   INDUSTRIAL  DESIGN. 


a  curved  outlet,  g,  likewise  terminating  in  flanges,  to  which  the 
discharge-pipe  is  secured.  The  piston,  or  bucket,  of  this  pump  is 
composed  of  a  brass  ring,  or  short  cylinder,  H,  upon  the  outer  cir- 
cumference of  which  is  formed  a  groove,  b,  (fig.  2,)  to  receive  a 
packing-ring,  c,  which  fits,  air-tight,  to  the  inside  of  the  pump 
cylinder.  The  bucket,  H,  has  also  a  central  partition,  d,  to  the  top 
of  which  arc  jointed  the  two  clacks,  I,  which  rest  upon  inclined  seats, 
formed  by  the  elevated  sides,  e,  of  the  bucket.  This  is  further  cast 
with  a  bridle,/,  perforated  in  the  middle,  to  receive  the  screw-bolt, 
g,  which  secures  it  to'  the  stout  hollow  piston-rod,  j.  This  rod, 
which,  in  the  generality  of  pumps,  is  made  of  but  small  diameter, 
like  the  upper  part,  K,  of  the  one  represented  in  the  plate,  is,  in  the 
present  instance,  of  a  sectional  area,  equal  to  half  that  of  the  pump 
cylinder.  It  follows  from  this,  as  will  be  more  particularly  ex- 
plained further  on,  that  the  water  is  discharged  during  both  the  up 
and  down  stroke  of  the  piston. 

The  clacks,  F,  have  projections,  h,  cast  upon  them,  which  pre- 
vent their  opening  too  far,  and  falling  over  against  the  sides  of 
the  casing,  B,  so  as  not  to  shut  again  when  required  to  do  so. 
The  clacks,  I,  in  the  bucket,  have  similar  projections,  i,  for  a  like 
purpose,  these  projections  striking  against  the  top  of  the  bridle,/, 
when  the  clacks  open.  It  will  have  been  observed,  that  the  seats 
of  these  valves  are  inclined  at  an  angle  of  45°,  with  the  view  of 
facilitating  their  opening  movement,  and  diminishing  the  concus- 
sive  action  of  their  own  weight.  The  edges  of  the  valve-seats  are 
generally  defended  with  a  strip  of  leather,  to  facilitate  their  tight 
closing. 

Figure  2  represents,  detached  and  in  elevation,  the  bucket,  H, 
with  it?  chicks,  i.  Fig.  3  is  a  horizontal  section  of  the  bucket,  taken 
at  the  line,  1 — 2.  Figs.  4  and  5  give  the  details  of  the  valve-scat, 
E,  in  elevation  and  plan,  the  clacks  being  removed. 

To  prevent  the  entrance  of  air  to  the  pump  cylinder,  it  is  closed 
at  the  top  by  a  cast-iron  cover,  L,  which  is  fitted  with  a  stuffing- 
box  for  the  passage  of  the  piston-rod ;  the  packing  is  compressed 
by  the  gland,  M,  similar  in  general  form  to  that  represented  in 
.Plate  XI.  (81.) 

ACTION   OF   THE    PUMP. 

406.  The  upper  extremity  of  the  piston-rod,  K,  carries  a  cross- 
head,  1,  (fig.  6,)  and  is  there  jointed  to  the  lower  extremity  of  a 
connecting-rod,  N,  which  is  itself  jointed  to  the  pin  of  a  crank,  o  ; 
this  latter  is  mounted  on  the  end  of  a  horizontal  shaft,  p,  actuated 
by  a  continuous  rotatory  movement.  This  movement  is  trans- 
formed by  means  of  the  crank  and  connecting-rod  into  an  alternate 
rectilinear  motion — that  is,  into  the  up-and-down  strokes  of  the 
pump  bucket — this  last  being  forced  to  move  in  a  straight  line,  the 
cross-head,  I,  sliding  in  vertical  guide-grooves,  to  maintain  the 
piston-rod,  K,  in  the  same  line  with  it. 

It  follows,  from  this  disposition  of  parts,  that  when-  the  crank, 
o,  is  in  the  position,  p — o,  fig.  6,  the  piston  will  be  at  the  bottom 
of  its  stroke,  that  is,  at  h'  ;  consequently,  during  the  time  the 
crank  turns,  the  piston  must  rise,  tending  to  leave  a  vacuum  below 
it,  because  the  space  between  the  clacks,  f,  and  its  under  side 
increases,  as  well  as  the  volume  of  air  that  may  be  therein  en- 
closed. Consequently,  the  pressure  of. this  air  upon  the  clacks 
k  diminished,  whilst  that  upon  the  surface  of  the  water  remains 


the  same,  and  causes  the  water  to  rise  up  the  suction-pipe,  and, 
raising  the  clacks,  F,  to  enter  the  pump  cylinder,  filling  it  up  nearly 
to  the  under  side  of  the  piston ;  or  if  the  apparatus  is  in  a  perfectly 
air-tight  condition,  it  will  rise  quite  up  to  the  piston. 

When  the  crank  has  reached  the  position,  p — 12, — that  is, 
when  it  shall  have  described  a  semi-revolution, — the  piston  itself 
will  likewise  be  at  the  highest  point  of  its  stroke,  and,  in  this 
position,  all  the  space  left  behind  it  in  the  body  of  the  pump  will 
be  filled  with  water;  if  now  the  crank,  continuing  its  rotation, 
makes  a  second  semi-revolution,  the  piston  will  descend,  and, 
pressing  upon  the  water  below  it,  will  cause  the  clacks,  f,  to 
shut.  Now,  as  the  water  is  incompressible,  it  must  find  an  exit, 
or  else  prevent  the  descent  of  the  piston ;  and  it  therefore  raises 
the  bucket-clacks,  i,  thus  opening  up  for  itself  a  passage  through 
the  piston,  h,  above  which  it  then  lodges.  But  as  the  piston-rod, 
J,  is  of  a  large  diameter,  and  therefore  occupies  a  considerable 
space  in  the  pump  cylinder,  a  part  of  the  water  must  necessarily 
escape  through  the  outlet,  g,  in  such  a.  manner  that,  when  the 
piston  shall  have  reached  the  bottom  of  its  stroke,  there  will  not 
remain  in  the  pump  cylinder  more  than  half  the  quantity  of  water 
which  was  contained  in  it  when  the  piston  was  at  the  top  of  its 
stroke. 

Such  is  the  effect  produced  by  the  first  turn  of  the  crank,  which 
corresponds  to  a  double  stroke  of  the  piston — that  is,  an  ascent  and 
a  descent. 

At  the  second  turn,  when  the  piston  again  rises,  it  sucks  up,  as 
it  were,  anew,  a  volume  of  water  about  equal  to  the  length  of 
cylinder  through  which  it  passes,  because  the  suction-clacks,  f, 
u  hich  were  shut,  now  open  again,  and  the  bucket-clacks,  i,  w  hicli 
were  open  during  the  descent,  are  now  shut  by  the  upward  move- 
ment of  the  piston. 

During  this  stroke,  all  the  water  which  previously  remained  above 
the  piston,  finds  itself  forced  to  pass  off  through  the  pipe,  G,  so 
that,  with  this  arrangement  of  piston  and  rod,  or  plunger,  of  large 
dimeter,  it  follows  that,  at  each  up-stroke  of  the  piston,  the  quan- 
tity of  water  which  rises  into  the  pump  is  equal  to  the  length  of 
cylinder  through  which  the  piston  passes,  the  half  of  which  quantity 
rises  in  the  discharge-pipe  during  the  descent,  and  the  other  half 
during  the  subsequent  ascent  of  the  piston,  and  the  jet  is  conse- 
quently rendered  almost  continuous  and  uniform. 

When,  on  the  contrary,  the  piston-rod  is  made  very  small  in 
diameter,  as  in  ordinary  pumps  (fig.  6),  the  discharge  of  the  water 
only  takes  place  during  the  ascent  of  the  piston,  and  it  is  conse- 
quently intermittent. 

In  a  pump,  as  in  all  other  machines  in  which  an  alternate  rec- 
tilinear is  derived  from  a  continuous  rotatory  motion,  by  means 
of  a  crank  and  connecting-rod,  the  spaces  passed  through  in  a 
straight  line  by  the  piston  do  not  correspond  to  the  angular 
spaces  described  by  the  crank-pin  ;  in  fact,  it  will  be  seen  'from 
the  diagram,  fig.  6,  that  if  the  crank-pin  is  supposed  to  describe 
a  series  of  equal  arcs,  beginning  from  the  point,  0,  the  correspond- 
ing distances,  0'  1',  1'  2',  2'  3',  passed  through  by  the  piston  will 
not  be  uniform ;  very  small  at  the  commencement  of  the  stroke, 
they  will  gradually  increase  towards  the  middle,  after  passing 
winch  they  will  simUarly  decrease  whilst  the  piston  approaches 
the  other  end  of  its  stroke.      The   successive   positions  of  the 


140 


pUtno  may  be  obtained  by  desrriblne;  villi  rarli 

lr.-«,  u»  i  » ilh  a  rm.hu.  equal  ' 
•rn. .  of  arc. 

-       i  -iU-'l"  of  u. 

oa  the  same  brie,  at  diioano  • 

the  length  of  the  piaton-rod,  measured  from  tin-  j-.int.  . 

bottom  of  the  pi%ton. 

-1,  that,  in  Co: 

of  the 

endtarouml  to  abow  the  Ml 

■paratrra  *olu  :  watar 

at  »oec.  Je-aclino  pump,  such  as  lb' 

upon  any  lino,  x  y,  as 
many  equal  parts  as  we  have  taken  in  diriaions  on  tin-  circle  <lc- 
- 
3,  4,  dr..  ll  of  the 

the  pi-'  -.  tin-re  i-  nothing  to  indicate 

- 

..■    i    :..     |    -•    :.    b  I.  i'.  «ill   pro- 

■  ■:•  r.  d  tli'  n,  that  when  it  Ins 

i  .'  to  1 1  ,  tin'  ijimutity 

t  may  l«-  represented  by  it-  : 

1 1  — I  j'.     It  i-  off  from 

>r  drawn  through  the  point,  13;  in 

di  Kcnda  from  11'  to  In',  it  is 

iltiplied  by  the  height, 

11' — l"  -   iff  from  the  point,  14  to  b.     It 

i  proceed    _•■■•.    hi  the  dia  {ram,  it  is 

*imply  ■  i  of  the  perpeudiculara  drawn 

15,  16,  17, 1 

I  for  each  portion 
e  prop  irtional  to  the  d 

the  cylinder  remaining 
wmrtint 
if.  through  the  vnr  7,  obtained  in  this 

i  surface 

ide,  and  which  will  give 

,  orrt  ipondcDce 

with  at  I  I  (be  rotation  of 

this    up- 
«  tin-  down-at 

tar  then 
:  i  curve  equal  I 

■ 

■ .  pumping  ap 
■I  ini  ia  tooh/thal  the  , 


ibcd  by 

-  i  rideat  that  the  product  ol  i 

that  "He  at  the  pistons,  hat 
.  brj .  the  eurve,  a 

niie  linn.' 

abed;  so    that   tin*  diagram  only  d  7,  ill    that  the 

i    and  lit  to  1-.  ill  the  latter,  are 

In  the  formor  filled  up  by  an  equal   h.  ■■•  an  equal  llal 

diagram  of  the  perfutniaaM  of  a  two<yiinder  pomp  may 

ting  that  of  the  |'Uiup.  fig.  I.  whieh, 
of  it-s  trunk  piston-rod,  acta  as  a  duubloacling  pump,  as 
already  explained, 

•  nis  the  diagram  of  the  perfbrmai 
cylinder  pomp,  of  whieh  the  pistons,  n.  a',  n',  represented,  tor 
eonvenii  i  in  the  same  cylinder,  occupy  the  i 

eorr.  jponding  I  three  crank-pins,  u.  0*,  0',  at 

at  the  angles  of  an  equilateral  triangle,  inscribed  in  i 
described  by  them  with  the  centre,  p.     In  of  Una 

disposition,  there  are  at  one  time  two  and  one 

.   and   at   another  time,   on    the   contrary,  only   one 
ascending  ami  two  deaoendi  to  represent  the  com- 

him  .1  performanoe  of  these  pumps  in  a  diagram,  by  tising  different 
ei. h.urs,  or  different  di  ptha  of  dude,  for  tin  !■< n. in 

dent  upon  tie  •    liTaken  up  by 

.   crank-pins,     l  nfuaion  will  be 

.  and  it  will  be  necessary  to  timl  the  positions,  a,  ■ 
the  attachment  of  tin-  connecting-rod  to  the  piston-rod  upon  the 

Vertical  line  penning  through  the  centre,  i,  01 

a*  the  distances  will    he  the  same   for  all,  being  mi 

different  parts  of  the  diagram. 

In  the  diagram,  t i ^ .  l".  we  haw  laid  down  the  performance  of 
each  of  tin-  three  pumps,  supposing  them  all  to  he  of  the  asms 
diameter,  and  taking  care,  when  two  pumps  aredischai 
gether,  to  add  together  their  performanoe  ;  thus,  for  example,  w  Inn 
on,-  of  tin-  pis  ruantitj  of  wati  r,  ■  •       , 

the  perpendicular,  13a,  that  which  . 
time  furnishes  a  qnantil]  expressed  bj  the  diatani 

quently,  the  total  rolun f  tl 

aented  In  the  total  height,  18a  :  when,  on  the  other  hand, 

of  the    three    pumps  d 

byaaingli  length  of  perpendicular,  such ai  It  will  be 

I,  thai  il  is  precisel]  at  the   moment    when   onlj  0 

out  its  maximum  performani 

which  it  follows,  that   the  jet    of  water  is  continuous,  an. I   almost 

uniform  throughout  its  duration, as  will  he  \rr\  evident  ir'.m  a 
consideration  of  the  >■■.  i  I,  tin-  outline  <.t  which  ii 

mined  by  pcrpendioulara,  or  ordinab  -.    n  to  the 

str.ii-ht  line,  m  ii,  thro 

mpars  the  oombinod  ofleel  of  a  three-cylinder  pump  with 
pumps,  we  have,  in  i 

. 


BOOK  OF  INDUSTRIAL  DESIGN. 


141 


merits;  and  it  will  be  remarked,  that  although,  with  cylinders  of 
an  equal  sectional  area,  we  necessarily  obtain  a  much  larger  dis- 
charge, yet  the  regularity  of  volume  is  not  so  great  as  in  the 
previous  example. 


STEAM  MOTORS. 

HIGH-FF.ESSURE    EXPANSIVE    STEAM-ENGINE. 

Plates  XXXVIII,  XXXIX.,  and  XL. 

407.  When  the  steam  generated  in  a  boiler  is  led  into  a  vase  or 
cylinder  which  is  hermetically  closed,  it  acts  with  its  entire  expansive 
force  upon  the  sides  and  ends  of  the  cylinder,  so  that,  if  this  en- 
closes  a  diaphragm,  or  piston,  capable  of  moving  through  the  cylin- 
der in  an  air-tight  manner,  the  force  of  the  steam,  in  seeking  to 
enlarge  its  volume,  will  make  the  piston  move.  It  is  in  this  way 
that  a  mechanical  effect  is  derived  from  the  expansive  action  of  the 
steam,  and  it  is  on  the  same  principle  that  the  generality  of  steam- 
engines  are  constructed. 

Thus,  in  most  apparatus  to  which  this  name  is  given,  the  action 
of  the  steam  is  caused  to  exert  itself  alternately  on  the  upper  and 
under  surface  of  the  piston,  enclosed  in  the  cylinder,  thereby  caus- 
ing it  to  make  a  rectilinear  back  and  forward  movement  or  stroke. 
(187.) 

Steam-engines  are  said  to  be  low  or  high  pressure  engines, 
according  as  the  tension  of  the  steam  is  only  of  about  1  atmosphere 
on  the  one  hand,  or  of  2,  3,  and  upwards,  on  the  other.  Low- 
pressure  engines  are  generally  condensing  engines,  and  high-pres- 
sure ones  non-condensing ;  so  that  the  terms,  low  pressure  or  con- 
densing, high  pressure  or  non-condensing,  are  used  indiscriminately, 
although,  in  modern  engineering  practice,  what  are  called  high- 
pressure  condensing  engines  are  extensively  employed. 

When  the  steam  is  made  to  act  alternately  above  and  below  the 
piston,  the  engine  is  said  to  be  double-acting ;  and  of  this  description 
are  most  of  those  employed  at  the  present  day ;  but  if  the  steam 
acts  only  on  one  side  of  the  piston,  as  is  the  case  in  many  mine- 
pumping  engines,  the  engine  is  called  a  single-acting  one. 

Low-pressure  engines  are  generally  also  condensing  engines; 
that  is  to  say,  that  after  the  steam  has  exerted  its  expansive  action 
upon  the  piston,  and  is  on  its  way  out  of  the  cylinder,  it  passes  into 
a  chamber  immersed  in  cold  water,  and  termed  a  condenser,  where 
it  is  condensed  or  reduced  to  the  state  of  water.  This  condensa- 
tion produces  a  partial  vacuum  in  the  cylinder,  and  consequently 
considerably  diminishes  the  resistance  to  the  movement  of  the 
piston. 

In  high-pressure  engines,  the  steam  which  has  produced  its  effect 
upon  the  piston  escapes  directly  to  the  atmosphere,  so  that  the  pis- 
ton has  always  to  overcome  a  resistance  equal  to  one  atmosphere, 
or  about  15  lbs.  per  square  inch,  acting  in  a  direction  opposite  to 
its  motion. 

Steam-engines  are  further  distinguished  as  expansive  and  non- 
expansive  ;  of  the  latter  description  are  those  wherein  the  steam 
enters  the  cylinder  throughout  the  entire  stroke  of  the  piston  ;  so 
that  the  pressure  is  uniform,  since  the  volume  of  steam  of  a  given 
pressure  which  enters  is  always  equal  to  the  space  passed  through 
by  the  piston. 


In  expansive  engines,  on  the  contraiy,  the  steam  is  only  allowed 
to  enter  the  cylinder  during  a  portion  of  the  stroke ;  so  that  the 
expansive  power  of  the  steam  is  called  into  action  during  the 
remainder  of  the  movement. 

The  machine  detailed  in  Plates  XXXVIII.,  XXXIX.,  and  XL., 
is  a  high-pressure  engine,  with  a  variable  expansion  valve. 

Fig.  1,  Plate  XXXVIII.,  represents  an  external  elevation  or  front 
view  of  the  machine,  the  frame  of  which  consists  of  a  hollow  column, 
with  lateral  openings. 

Fig.  2  is  a  horizontal  section,  taken  at  the  height  of  the  line, 
1—2. 

Fig.  3  is  an  elevation  of  a  fragment  of  the  lower  part  of  the 
column. 

Fig.  4  is  another  horizontal  section,  taken  at  the  line,  3 — 4;  and 
fig.  5  is  an  elevation  of  the  capital  of  the  column. 

Figs.  6  and  7  are  diagrams,  relating  to  the  movement  of  the 
governor,  with  its  balls. 

Fig.  8,  Plate  XXXIX.,  represents  a  vertical  section,  taken 
through  the  axes  of  the  column  and  the  steam  cylinder,  at  the  plane, 
5 — 6,  parallel  to  that  of  the  fly-wheel. 

Fig.  9  is  another  vertical  section,  at  right  angles  to  the  preceding 
figure. 

And,  finally,  fig.  10  is  a  horizontal  section,  taken  at  the  broken 
line,  7 — 8—9—10. 

This  machine  consists  of  a  cast-iron  cylinder,  a,  truly  boied  out, 
and  enclosing  the  piston,  B.  On  one  side  of  the  cylinder  are  tast 
the  passages,  a,  A,  by  which  the  steam  enters  alternately  above  :.nd 
below  the  piston.  These  passages  are  successively  covered  over 
by  a  cup  or  valve,  d,  the  details  of  which  are  given  in  figs.  28  to 
31,  Plate  XL.;  and  the  valve  is  itself  contained  in  the  cast-iron 
chamber,  E,  called  the  valve  casing,  and  communicating  with  a 
second  chamber,  F,  called  the  expansion-valce  casing ;  it  is  inio 
this  latter  chamber  that  the  steam  is  first  conducted  by  the  pipe, 
G,  from  the  boiler.  The  communication  between  the  two  vah  o 
casings  is  intercepted  for  short  periods  during  the  action  of  the 
machine,  by  the  expansion  valve,  h,  detailed  in  figs.  38  to  4 1  > 
Plate  XL. 

The  vertical  rod,  i,  of  the  piston,  b,  is  attached  at  its  upper  ex- 
tremity to  a  short  cross  pin,  e%  which  connects  it  to  the  wrought- 
iron  connecting-rod,  j,  hung  on  the  pin,  /,  of  the  crank,  k  ;  this  is 
adjusted  and  keyed  upon  the  extremity  of  the  horizontal  shaft,  t, 
which  carries  on  one  side  the  fly-wheel,  in,  and  on  the  other  the 
eccentrics,  n,  o,  p.  The  first  of  these  eccentrics  is  intended  to  ac- 
tuate the  distributing  valve,  D,  the  rod,  g,  of  which  is  connected  to 
it  by  the  intermediate  adjustable  rod,  n'.  The  second  works  the 
expansion  valve,  H,  by  means  of  the  rods,  o'  and  h ;  and,  finally,  the 
third  eccentric,  p,  gives  an  alternate  movement  to  the  piston  or 
plunger,  Q,  of  the  feed-pump,  r. 

The  steam  cylinder  is  bolted  in  a  firm  and  solid  manner,  by 
its  upper  flanges,  to  the  top  of  the  hollow,  cast-iron  plinth  or  pe- 
destal, s,  on  which  also  rests,  and  is  bolted,  the  column,  t.  The 
pedestal  is  square ;  and,  at  the  corners  of  its  base,  lugs  are  east, 
by  means  of  which  it  is  firmly  bolted  down  to  a  solid  stone 
foundation.  • 

The  column,  T,  is  cast  hollow,  and  with  four  large  lateral  open- 
ings diametrically  opposite  to   each  other,  their   object  J»einc  t« 


THE    1 


the  m  r.-^.i  of  the  column,  and  to  afford  the  a«reaaary 
>  for  the  mtr.-lu  U  a  ..f  th.   various  piece*  when  b.  h 

arfcaa  uJu-d  down.  This  coluraa  aiao  serves  aa  a 
frame  for  la*  aotira  machine,  and  abovs  the  capital  in  placed  a  east- 
anas  piDow-hlcMk,  i\  furoi»h.d  with  bearing  braaat  - 

.  jownal  of  the  first  motion  shaft,  aa  well  aa  the  supporting 
bracks**,  a,  f,  of  the  spindle,  /,  of  the  bail  f 

■ida  are  alao  boiled  the  two  supports,  i,  of  the  parallel  inolion,  and 
■dig- 

I   or  THE  MX 

408.  Before  proeee  i  I  shall  give  some  idea  of  tho 

fee  era!  action  of  the  machine.     Aa  already  mentioned,  the  steam 
ia  generated  in  a  bod-"  uiije,  as  that  represented  in 

QT,     189  .   i'-l    -  ■  tondneted  by  t:  <;,  into 

tne  first  chamber,  r ;  « 
toe  orifice,  or  port,  ,1.  the  steam  finds  its  way  into  1 

.•it  passes  either  to  the  nj  bwat  and  ..I" 

•r  other 
of  the   :  ~   loaaagea,  a,  b.     Now,  whe  n   the  |  , 

is  almost  fully 
nel,  b,  U  in  communication   with 

■•■.lli.h    the    tWl  '  tdocl    it    tO    thl 

I  •        it      i  to  the  cylinder,  it  has 

a  pressure  of,  nay  four  '  will  set  upon 

-  •  ■  oe,  bow- 

in  commtuiea- 
■ ,  •  ■  |  iial  to 

M>e  atmosphere  oppo-  ire   the  actual 

l>ressur»  acting  on  tlie  lop  ..f  the  piston  will  ba  I 

•  rs  the 
Km  psasage,  6,  te ,  allow  the   - 
of  the  ej  ■■  .it.  is  |nit  in  communication  with  the 

.  the  rup  of  •  Bar  the 

steam  which  has  just  acted  on  the  upper  tide  of  Liu-  pist.jn  during 

■  be  remarked,  that  if  the  intr.xlurti.>n  of  the  steam  takes 

place  do  up-and-down  stroke  of  the  piston,  which 

.  communicated  directly  with 

!'.  k.  pi  one  of  the  porta  oneo- 

i  would 

i  arid  that  the  machine 

waa  a  hi  —'.hat  is  to  say,  tli.it  it 

I  with  a  full  ■  ■  .un. 

In  the  mnli 

■ 

with  lie 

• 
at  the  |  the  passage,  d,  mu-t  ngOMBl  in  ^ 

expand  |ng  the 

I  to  be 

in   this    rn.se  a 

a  (bird,  half. 


thirds    of   the   capacity  of   the   cylinder,  aeeordiug  as  the  intro-  . 

iiird,  ouc-haJl 
il  is  the  ratio  between  tin-  qnantitj 
re  ssun-  Ultluduued,  and   lie    ■ 
der,  which  expresses  the  degree  of  expansion  at  which  the 

works. 

rARALLEL    MOT10*. 

409.  Tlie  rectilinear  altsmal  ■  trans- 

Ibnned  into  a  eontinuoui  circular  motion  on  the  Beat  motion  abaft, 
I.  ley  the  interv, utii.n  of  tie-  nnnnffflrtlia; rnd,  J,  and  crank,  i;  hut 
with  this  arrni  is  naturally  a  lateral  strain  u|sen  the 

top  of  the  pisteo-rodt  I,  ami   in   onlrr  tliat  its  movement  may  be 
.  rcctiliuear  and  vertical,  it  la  jointed  :  articu- 

lated levers,  fanning  what  i-  termed  a  parallel  motion. 

•    I  of  two  wrought  mm  rod- 

i,  and  are  articu- 
lated at  tin  ir  opposite  BXtreflaif  -.  x.  mar  their  middle, 

nnd  are  jointed  at  one  end  to  the  I  ross  pin,  e",  fig.  9,  of  Um 

rod  end  ;  and  at  tl tin  r  to  the  rod,  v,  attached  to  a  cross. 

o  a,  and  oscillating  in  1«  snogs,  in  ■  * 
bolted  to  the  lower  part  of  th* 
Xlii-  heed  of  this  laet-mentioned  — Hiatt»g  rod  is  ,i.  ..died  sepa- 

ratelj,  hi  XL      1 1  has  brasses,  to  < 

the  journal  of  i :  '   by  which  U  ia  eonneoted  to  the  ends 

Of  tlie  II   ■ 

•mbination   of  this   n  inch,  that   the  point  of 

attachment,  r,  constantly   mo?i  '   line   throughout  the 

entire   stroke.      It    ma;,  metrical   prim 

:  in  the  diagrams,  li^'s.  8  and  11.     T 
•opposed,  that  alter  baring  drawn  the  horizontal  line,  t1  /\  and  tho 
vortical,  t  >',  distances,  e  t?  and  t  c',  are  set  off  00   the  ktttl 
to  the  half  stroke  ..I  the  piston,  or  to  the  radius  of  the  crank  ;  then, 
with  the  points,  r  r\  describe  Bfl  are.  with  a  radius,  e  /-equal  to  the 

length  of  the  lever,  x.  which  is  taken  at  pleasure,  but  should  never 
man  the  stroke  of  the  piston.    If  we  nasi  lay  off  this 

from  e"  to  /»',  the  space.  ;/  ;.',  will  express  the  amount  of 
oscillation  of  the  rod,  Y,  the  centre   I  Inch  wo 

place  below,  on  the  vertical   line,  drawn  at  an  equal  disl.-ua  N  (rom 

and  between  tin-  two  points,  a,  p*.    We  next  As  the  point,  n,  of 

attachment  of  the   rccU,  \.  ].,  the   h\c  r,  x.     This  point,  n,  during 
■  inc  tit  of  the  parallel  motion,  nisessarily  decicribes  a  circu- 
lar arc,  of  which  it  is  requisite  tec  find  the  centre.     In  invi  - 
ibis  problem,  it  ia  tec  !*•  observed  that,  whatever  may  l><-  • 
tic.n  cci  the-  Icier,  the  point,  "  ■■  from 

the   eatremlty,  ;■.  or  tl th.-r  one,*    If,  then,  we  in  in 

draw  ti.-  ';'''•  indkwHng  the  difierei 

:  the  lc  \er,  c-.crr  ■ '.  ■*.  «*,  of  tie- 

r's! cii'l.  we  shall,  on  each  "t   tie  SS  lines,  obtain   the-  s.  \cral  posi- 

m',  a*,  ii',  by  laying  off  oa  fliem  dhoai  ««f  tin-  d 

;>  n  or  r  n.      We  can  then    M  ry    easily   linel   the   centre   of  tho  sro 

passing  through  tin  M  points.  (10.) 

cm  of  an  snalogOUl  parallel  motion, 
:n  which  the  riMls,  V,  art  so  eli-pose.l.  that  their  point  of 
:it  is  exactly  iii  the  D  x;  aid  in  this 


BOOK   OF   INDUSTRIAL  DESIGN. 


case,  their  axis  of  oscillation  lies  in  a  plane  passing  through  the 
vertical  axis,  e  e3. 


DETAILS  OF  CONSTRUCTION. 

STEAM   CYLINDER. 

410.  The  cylinder  is  cast  in  one  piece  with  its  bottom  cover  and 
lateral  steam  passages.  As  it  should  be  bored  with  great  care,  so 
as  to  be  perfectly  cylindrical  in  the  interior,  a  central  opening  is 
made  in  the  bottom  for  the  passage  of  the  spindle  of  the  boring 
tool ;  this  opening,  however,  is  afterwards  closed  by  the  small 
cover,  a3,  cemented  at  its  junction  surfaces,  and  bolted  down  to  the 
bottom  of  the  cylinder.  The  upper  end  of  the  cylinder  is  closed 
by  a  cast-iron  cover,  a',  which  is  formed  into  a  stuffing-box  in  the 
centre,  to  embrace  the  piston-rod,  which  works  steam-tight  through 
it.  The  packing  is  compressed  or  forced  down  for  this  purpose 
by  a  gland  (140),  bolted  to  the  stuffing-box,  and  hollowed  out  at 
the  top  to  receive  the  lubricating  oil.  The  valve-face,  on  the  out- 
side of  the  cylinder,  and  on  which  the  valve  works,  is  planed  very 
carefully,  so  as  to  be  a  true  plane  throughout.  The  same  is  done 
with  the  valve-casing  at  the  flanges,  where  it  is  fitted  to  the  valve- 
face. 


The  piston  (figs.  8,  9,-19,  and  20)  is  composed  of  two  cast-iron 
plates,  which  have  an  annular  space  between  them  for  the  recep- 
tion of  two  concentric  cast  or  wrought-iron  or  brass  packing-rings, 
c'.  These  rings  are  cut  through  at  one  side,  and  are  placed  one 
within  the  other  in  such  a  manner,  that  the  breaks  in  each  are 
diametrically  opposite  to  each  other;  their  thickness  gradually 
diminishes  on  each  side  towards  the  break,  and  they  are  hammered 
on  the  inside  in  a  cold  state,  which  renders  them  elastic,  giving 
them  a  constant  tendency  to  open.  Since  the  diameter  of  the 
outer  ring  is  equal  toihat  of  the  cylinder  when  the  two  edges  are 
brought  together,  the  elasticity  of  the  inner  ring,  combining  with 
that  of  the  outer  one,  tending  constantly  to  enlarge  them,  it 
follows  that  there  must  be  a  perfect  coincidence  between  the 
outside  of  the  ring  and  the  inside  of  the  cylinder  throughout  the 
whole  extent  of  the  latter.  Thus  the  contact  of  the  piston  with 
the  sides  of  the  cylinder  only  takes  place  through  the  packing- 
ring,  and  not  by  the  plates,  which  are  of  a  slightly  less  diameter. 
To  prevent  the  passage  of  the  steam  through  the  break  in  the 
outer  packing-ring,  a  rectangular  opening  is  made  in  the  two  edges 
of  the  ring,  and  in  this  is  placed  a  small  tongue-piece,  a',  screwed 
to  the  inner  ring,  this  piece  serving  to  close  or  break  the  joint 
without  preventing  the  play  of  the  rings.  The  principal  plate  of 
the  piston  is  fixed  to  the  piston-rod  by  means  of  a  key  (fig.  9)- 
The  piston-rod  is  consequently  of  increased  diameter  at  its  lower 
end.  The  upper  end  of  the  piston-rod  is  likewise  fixed  in  a  socket, 
l',  (figs.  9  and  13,)  which  terminates  in  two  vertical  branches  to 
receive  the  middle  of  the  spindle,  e1,  which  is  held  down  by 
means  of  a  key. 

CONNECTING-ROD   AND    CRANE. 

411.  Tne  connecting-rod,  J,  (figs.  8,  9,  14,  and  15,)  terminates 
at  its  lower  end  in  a  fork,  by  means  of  which  it  is  jointed  to  the 


spindle,  e3,  brasses  being  fitted  in  either  side,  and  secured  by  bridle- 
pieces  passing  under  them  and  keyed  above.  The  fork  is  jointed 
to  the  spindle,  ea,  on  each  side  of  the  piston-rod  head,  sufficient 
space,  however,  being  left  between  them  for  the  levers,  x.  The 
head  of  the  connecting-rod  (figs.  15  and  16)  is  likewise  fitted  with 
brasses  to  embrace  the  pin,  /,  of  the  crank ;  these  brasses  are ' 
tightened  up  by  means  of  the  pressure  screw,/'. 

The  crank,  K,  like  the  connecting-rod,  J,  is  of  wrought-iron, 
being  adjusted  on  the  end  of  the  first  motion  shaft,  and  secured  to 
it  by  a  key.  This  crank  is  very  often  made  of  casHron  in  sta- 
tionary engines,  but  in  marine  and  locomotive  engines  it  is  gene- 
rally forged,  so  as  to  be  better  suited  for  resisting  severe  strains 
and  shocks. 

The  first  motion  shaft,  l,  is  likewise  either  of  cast  or  wrought- 
iron.  In  the  notes,  we  have  already  given  u.bles  and  rules  for 
determining  the  respective  dimensions  of  this  detail.  It  is  not 
only  supported  by  the  brasses  of  the  pillow-block,  v,  but  also  by 
those  of  a  similar  onev  fixed,  we  shall  suppose,  upon  the  wall 
which  divides  the  engine-house  from  the  workshop  or  factory.  It 
should  always  be  larger  in  diameter  where  it  receives  the  fly- 
wheel, M. 

FLY-WHEEL. 

412.  The  fly-wheel  is  of  cast-iron — of  a  single  piece  in  the  pre- 
sent example,  because  its  diameter  is  only  3-5  metres.  When  of 
larger  dimensions,  the  rim  and  the  arms  are  cast  in  separate  pieces, 
and  then  bolted  together.  For  wheels  of  from  5  to  8  metres  in 
diameter,  the  rim  is  made  in  several  pieces,  and  the  arms  are  also 
cast  separate  from  the  boss,  and  all  the  parts  are  then  bolted 
together.  The  arms  are  sometimes  made  of  wrought-iron  of  small 
dimensions,  with  the  view  of  reducing  the  weight  near  the  centre, 
without  reducing  the  effect  of  the  wheel. 

FEED-PUMP. 

413.  This  pump  serves  to  force  into  the  boiler  a  certain  quantity 
of  water,  to  replace  that  which  is  converted  into  steam  and  expend- 
ed in  actuating  the  engine.  It  is  a  simple  force-pump,  consisting 
of  a  cylinder,  R,  in  which  works  the  solid  piston  or  plungci,  q. 
The  piston  is  not  in  contact  with  the  sides  of  the  pump  cylinder, 
and  the  latter  consequently  only  requires  to  be  turned  out  at  its 
upper  part,  where  it  is  formed  into  a  stuffing-box  aud  guide  for 
the  plunger,  being  necessarily  air-tight. 

On  one  side  of  the  pump  is  cast  a  short  pipe,  to  which  is  atl..Ji- 
ed  the  valve-box,  R,  generally  made  of  brass.  To  the  lower  part 
of  this  is  secured  the  suction-pipe,  t',  communicating  with  a  cistern 
of  water,  and  having  a  stopcock,  s',  upon  it,  like  the  one  repre- 
sented in  detail  in  Plate  XVII.  To  one  side  of.  the  valve-box  is 
likewise  fitted  the  discharge-pipe,  carrying  a  similar  stopcock,  s3 ; 
this  last  pipe  is  generally  passed  through  the  pipe  which  carries 
off  the  waste  steam,  so  that  the  water  may  take  up  some  of  the 
heat  of  this  steam  before  entering  the  boiler. 

It  will  be  seen,  from  figs.  9  and  23,  that  this  valve-box  contains 
two  valves,  s',  s2;  the  lower  one  of  which,  s',  is  the  suction  valve, 
and  the  upper  one,  s',  is  the  discharge-valve.  The  latter  is  much 
larger  in  diameter  than  the  former,  so  that  its  seat  may  be  wide 
enough  for  the  lower  valve  to  be  passed  through  it.     The  upper 


Tin.  !  nit.\i  cut: 


ecsJ  of  thr    tilii  -■<>!   U  tlowd  b>  I 
dowa  I  .  sod  ir..n  bndlr,  o*. 

.1    MM  to 
6l  ■<*•  ravly.     Th*  nodrr  part  ol  il,MM 

jiaasage 

tal,  nml 
ujx>n  the  li 

Th*  ■  1  null  rod,  t,  adjust- 

!.!  i r< >n  rod,  1', 
:i  cullnr, 
■ 

thai  ><(  the  pumps  of 

■  >ii.     Tim*,  wb<  n   tha 

and  1",  are  open,  the 

pipe,  k',  the  valve,  a*,  opening, 

lj  "i"  the  pump,  into  which  ii  H 

v. 

■ 

-  along  the  discharge-pipe  to 
i 

entirely  shot  off  by  closing  them ;  but 
die,  p,  with  it.-,  rod,  1  •',  will  continue 

■  bicb  is 
-      \.  1,  by  which  the  piston-rod 

Uittatl.  d,  in  such  a  manner  thai  the  socket, 

■■  rod,  r',  will  simply  slide  iij> 

BALL  nil   lOTATDra    I 

41 1.  '.'  tton  "f 

•  proportion  t"  tin-  n 

1  valve, 
throttle-valve.     Just 
for  I 

■  •in.  hi.  and  i-  actuated  by  ■  r. .'1.  passing 

■  steam 
der  mors  or  1.  r.- ;  sod,  similarly,  thu 

■  ■I  the  piston, 

li"ll  Willi  it 
1   as  -  .-ii  in  li:.'   1,  of  n  nil 

lupport,  /.'.  mid 

1  ■ . j .( ..  r  1 11.1  are 

In  cast- 

1 

1  ■-./.!..  tli.'  wroogbtiroo  "r  e  ipper 

iDudle: 

ind  tli" 
balls  l»  .nil  with   it,  will  bavi 


•ril  f,.rce 
- 
• 

up»n  tl 
is  to  SSJ 
■ 

the    bolls  will  fly  bai. 

I 
will   lx  circular 

tod  bell- 
s  1I1  the  throtl 

<■'.  drawn  with  it-,  bos,  a',  in  I 

ralre  will  be  slmt.     I 

d  below  tin-  |ir.i|N  r  point,  owing  t.j  an  iin-r.  ..- 
the  balls  will  approach  1  ad  assume  Ihi  1    • 

nend,  and,  consequently,  the 
throttle-valre  will  become  1.  1-  to  allow  ■ 

quantity  of  ah  am  t"  enb  r  the  vain 
Uir  c)  Under.     'I 
which  they  cann 
the  spindle,  /. 

The  motion  of  tliis  spindle  is  derived  from  the  lirst  motion  slmft, 
i„  by  in'  '.  fixed  upon  the  inti  n 

spindle,  r*,  pUo  capital  of  the  column,  t.  and  by  the 

bevil-whi  ng  their  motion  from  the  pulley,  r4,  • 

t  rati"  is  maintained  between  the  r.itr  of  the  mai 
that  of  the  governor. 

and  ".  will  sufficiently  explain 
tin-  respective  ]  10I  tl"  i"  ndulum,  and 

will  show  how  tin-  ri-  el  upon  the  spindle  li 

li_v.  and  is  in  proportion  t".  tli"  flying  asundor  of  t 
im;  to  'lie  number  of  n 

tin-  BUS]  ■ 


MOVEMENTS  OF  THE   DISTRIBUTION    AND  EXPAN- 
SION  \  M.\  is 

11;,    \'.  tli.it  tli.-  valve,  D,  represented  in  different 

and  "i.  and  i»  l«- ■  r i 
is  attached,  by  Its  rod,  g,  !•>  tli"  vertical  rod,  nf,  which  is  joined  t.. 

the  rod,  a*,  of  tli"  circular  "< Dtrie,n,  figs.  Bo^and  84.    Winn, 

sn  was  customary  until  lately,  tha  «-«-ntr«.  «»t*  Iheecc 

riuliiis  perpendicular  t.'  the  direction  nf  tli"  crank,  the  movements 

"i  tli"  st.  inn  piston  and  reive  ar"  different  t"  <  ach  oaher — that  is 

when  tha  crank  passes  from  the  lefl  boriaontal  t"  tk 
■ 

I 
of  tli"  vertical  line,  drawn  ilir..u„'li  the  centre  of  tl>"  firsl 

,:.l  eonsequenl 
tl"  rslvi  11  'it  quite  differonl  (■.  thai  ol 

too,  in  -  "  that,  when  il" 

»tr..k",  tli.  valve,  ""  tli"  otfai  r  band, 


BOOK    OF    INDUSTRIAL   DESIGN.- 


porta  are  consequently  fully  open,  to  give  the  steam  the  freest 
passage  into  the  cylinder. 

Whilst  the  piston  is  accomplishing  its  stroke  in  one  direction, 
the  valve  moves  up  or  down,  and  returns  again  to  its  central  po- 
sition, the  part  which  it  covered  being  opened  and  again  shut; 
when,  however,  the  crank  makes  two  fourths  of  a  revolution  in 
different  directions,  the  piston  rises  and  falls  half  a  stroke  each 
way,  whilst  the  valve  makes  a  single  rectilinear  movement  in  one 
direction.  * 

Finally,  for  each  of  these  movements,  whilst  the  velocities  of  the 
piston  are  increasing  from  the  commencement  towards  4he  middle 
of  its  stroke,  those  of  the  valve  are  decreasing,  and  reciprocally.  It 
therefore  follows,  that  the  maximum  space  passed  through  by  the 
piston,  for  a  given  portion  of  a  revolution  of  the  crank,  corresponds 
to  the  minimum  passed  through  by  the  valve. 

LEAD  AND  LAP  OF  THE  VALVE. 

416.  Of  late  years,  engineers  ha  re-  recognised  the  advantage  of 
inclining  the  radius  of  the  eccentric,  with  regard  to  the  radius  of  the 
crank,  instead  of  placing  them  perpendicular  to  one  another,  in  such 
a  manner  that,  at  the  dead  points — that  is,  the  extreme  high  and 
low  positions  of  the  piston — the  valve  shall  already  have  passed 
the  middle  of  its  stroke  to  a  slight  extent;  it  is  this  advance  of  the 
valve  which  is  termed  the  lead. 

The  effect  of  giving  this  lead  to  the  valve,  is  to  facilitate  the 
introduction  of  the  steam  into  the  cylinder  at  the  commencement 
of  the  piston's  stroke,  and  at  the  same  time  to  allow  a  freer  exit 
to  the  waste  steam  on  the  other  side  of  the  piston ;  a  greater  uni- 
formity of  motion  is  in  consequence  obtained,  whilst  less  force  is 
lost. 

In  order  to  avoid  as  much  as  possible  the  back  pressure  due  to 
the  slow  exit  of  the  waste  steam,  it  is  likewise  customary,  in  addi- 
tion to  the  lead,  to  give  the  valve  more  or  less  lap ;  that  is  to  say, 
to  make  the  width  of  that  part  of  the  valve  which  covers  the  ports, 
a,  i,  fig.  28,  sensibly  greater  than  that  of  the  ports  themselves. 

In  explanation  of  the  effects  due  to  the  lead  and  lap  of  the  valve, 
we  have,  in  fig.  35,  given  a  geometrical  diagram,  indicating  the 
relative  positions  of  the  crank,  the  piston,  the  eccentric,  and  of  the 
valve. 

Let  o  o  represent  the  radius  of  the  crank ;  with  this  distance  as 
a  radius,  and  with  the  centre,  o,  describe  a  semicircle,  which  divide 
into  a  certain  number  of  equal  parts.  From  each  of  the  points  of 
division,  let  fall  perpendiculars  upon  the  diameter,  o  c.  The  points 
of  contact,  1,  2,  3,  4,  &c,  represent  upon  this  diameter,  considered 
ss  the  stroke  of  the  piston,  the  respective  positions  of  the  piston, 
corresponding  to  those,  22,  3",  4a,  &c,  of  the  crank  pin.  It  is  un- 
necessary to  take  into  account  the  length  of  the  connecting-rod, 
which  connects  the  latter  to  the  piston,  because,  in  the  present  case, 
the  connecting-rod  is  supposed  to  be  of  an  indefinite  length,  and 
to  remain  constantly  parallel  to  itself,  so  that  it  cannot  modify  the 
results. 

With  the  centre,  o,  likewise  describe  a  circle  with  a  radius, 
o  a',  equal  to  that  of  the  eccentric,  N.  We  have  assumed  the 
point,  a',  to  be  the  position  the  centre  of  the  eccentric  should 
have  at  the  moment  when  the  piston  v  at  the  end  of  its  stroke — 


that  is  to  say,  at  o;  the  distance  of  this  point,  a',  from  Hi"  vertical 
m  n,  oxpresses  the  lead  of  the  valve,  and  consequently  the  angle 
m  o  a',  is  called  the  angle  of  lead.  The  position  of  the  point,  a' 
may  likewise  be  obtained,  after  .the  following  data  arc  decided  on— 
namely,  the  height  of  the  ports,  a,  b,  fig.  28,  the  width,  r  s,  of  the 
flange  of  the  valve,  which  is  equal  to  the  height  of  opening,  I  r 
which  properly  expresses  the  amount  of  lead  given  to  the  port 
augmented  by  twice  the  lap,  together  with  the  amount  of  the  intro- 
duction of  the  steam  to  the  cylinder,  and  the  amount  of  opening, 
s'  l',  expressing  the  lead  given  to  the  escaping  steam,  and  which  is 
always  greater  than  the  former,  so  that  the  exit  passages  may  he  in 
communication  as  long  as  possible. 

The  diameter  of  the  eccentric,  N,  is  equal  to  the  height  of  the 
port,  augmented  by  the  width,  r  s,  of  the  flange  of  the  valve,  and 
the  difference  which  exists  between  the  two  amounts  of  lead,  .s'  l' 
and  r  t;  it  is,  then,  with  the  half  of  this  as  radius  that  the  circle, 
a'  b'  c  d',  must  be  described ;  and  we  then  obtain  the  point,  «',  by 
setting  off  from  the  centre,  o,  to  the  right  of  the  vertical,  m  n,  a 
distance  equal  to  the  lead  of  introduction,  r  I,  augmented  by  the  lap. 
Starting  from  this  point,  a',  we  then  divide  this  circle  into  as  many 
equal  parts  as  we  previously  divided  the  one  into,  described  by  the 
crank  pin,  and  then  through  each  of  the  points  of  division  we  draw 
perpendiculars  to  the  vertical,  m  n. 

We  further  draw  the  straight  line,  a'  g',  parallel  to  m  n,  when 
the  distance  of  the  several  points  of  division  from  this  line  «iil 
indicate  the  successive  positions  of  the  valve  in  relation  to  those 
of  the  piston.  Thus,  after  having  drawn  the  horizontals,  r  u, 
through  the  extreme  point,  r,  of  the  valve,  at  the  moment  when 
the  piston  is  at  the  extremity  of  its  stroke,  make  1'— 1'  equal  to 
b'  J2,  and  the  point,  1',  indicates  how  far  the  valve  has  descended 
during  the  time  the  piston  has  traversed  the  space,  0  1,  whilst  the 
crank  has  described  the  first  arc,  o  1'.  In  like  manner,  set  off 
the  distances,  c1  c3,  dl  d2,  &c,  which  correspond  to  the  third  and 
fifth  divisions,  reckoning  from  the  horizontal  line,  r  n,  from  j2  to  3', 
and  from  h*  to  5',  on  the  verticals  corresponding  to  the  third  and 
fifth  positions  of  the  piston,  and  consequently  the  positions,  3* 
and  5",  of  the  crank.  It  will  then  be  seen  that  the  valve  con- 
tinues to  descend  until  the  moment  the  centre  of  the  eccentric, 
reaches  the  point,/',  upon  the  horizontal  line,  of,  corresponding 
to  the  sixth  position,  and  the  valve  then  wholly  uncovers  the 
port,  a,  as  shown  in  fig.  29.  During  the  continued  revolution  of 
the  eccentric,  on  passing  this  point  the  distances  of  the  points  of 
division  from  the  line,  a'  g',  diminish,  and  the  valve  reascends,  in 
such  a  manner  as  that,  w:hen  the  centre  attains  the  point,  p — that 
is  to  say,  when  the  crank  shall  have  performed  a  semi-revolution, 
and  the  piston  have  arrived  at  18,  at  the  other  end  of  its  stroke — 
the  valvo  will  occupy  the  position  indicated  in  fig.  30.  This 
figure  shows  that  it  uncovers  the  lower  port,  b,  for  the  introduc- 
tion of  the  fresh  steam,  and  the  upper  one,  a,  for  the  escape  of 
the  used  steam.  If  the  respective  positions,  6',  7',  8',  9',  ecc,  of 
the  valve,  be  determined  throughout  the  entire  stroke,  by  setting 
off  upon  the  verticals,  6,  7,  8,  9,  &c,  the  distances  of  the  points 
of  division  of  the  eccentric  from  the  straight  line,  a'  g',  as  already 
explained,  a  curve  will  be  formed,  as  at  u  3'  6'  9'  18',  which  is  a 
species  of  ellipse.  This  diagram  has  the  advantage  of  bringing 
into  a  single  view  the  relative  positions  of  the  crank,  piston,  eccen- 


■ 


tnr.  ia.1  valre,  »nJ  brtHulca  th*  determination  of  tf.*  pad 
lite  vslte,  <wm»puadin£  to  any  r»  - 

p.  of  the  -*— ■t-f8-'— .  U  U  aofficirnt  to  dnw  the  vertical,  y  x\ 

»h^h  will  enl  the  Ml 

Dais  point,  (ram  the  horizontal,  I  ■*, 

• 
by  the  boruooUl,  f  u. 

•,  wiih  a  valve 
is  lead  and  lap,  dvely  to 

it  off  at  four- 

-1  that,  if  the  machine  contio 

c  which 
■ 
attain  tl  I  soon  as 

■    :.      In   llii-   | 

open — tho  fir^t  to  the  exit  aperture, 

.  whilst  the  valve  ta  at 

found  by  continuing 

,18  -  l  BtV,  is  exactly 

u  16".     On  iho  same 

diagram  '9'  18', 

•  •juil  an  1   par.. 

:  the  v;iH«-.  in  : 

poaitioni 

upon  the  verti- 

<..!-,  drawn  till 
It  m.  . 

iran'.    It  i».  I  reduce  it  x-  g 

.  miuish  the  surface  of  the  valve,  and 

ii  the  hack  of  it-     In 
the  axil  port,  e, 
••  r  Uuui  tliat  nf  the  introduction  ;  mtity  at 

be  lap  an. I  the 
lead,  (  i  and  I  r. 

■ 
417   The  actios  of  - 
that  of  •  n  of  iU 

•  ilated  in  the  - 

■ 
1   u|N,n   tha  main  shaft,  u  n-  ■  .th  the 

to  the  adjuatab 
u*.    Thia  arrangement  allowi 
ihn.w  being  increased  or  din 

.     . 

•     It      To  thi- 
central 

If  •*•  •     !«•  in  the  MOM 


tioo  aa  the  cm: 
drawn  i 
35,  that 

tlian  would  oil 

.1  partis 
starting  from  i  •    through  the  point,  v1,  draw  a  i 

lino,  ami  then  eel  off  OH  the  varietal 

from   tl..  Urolith   the   D  .   of    the 

ii  m'  ■' ;.',  the 
:   which  i«  Sal — tinted  with  . 

- 

■  i  ill  Una 
drawn  throngh  the  npj  port,d,  in  the  point,  n,  whi  Ii 

-  at  what  time  the  va  entrance  port 

It  will  be  Been  tliat  thu  the  poaitian,  <V,  of  the 

■team-piston,  tl  ;  that  tho  cu 

a  has  performed  no  more  than  a  fourth  of  lot  I 

tinning  the  movement)  it  will  be  observed  that  the  valve,  ■,  b)bm 
bigber  and  higher,  so  that  it  b  rer  the  entranei 

little  before  tin  -  the  sad  of  Ha  stroke;  but  it  i*  evi- 

dent thai  ilie  steam  cannot  find  ita  wsj  into  the  eyiindar  at  this 
point,  for  the  distribution  vajve  is  in  its  turn  dosed,  as  s...  i 

bv  the  I  ■  and  of 

88  and  40,  and  h  shown  also  in  iho 
i 

n  of  it* 
■•  lativaly  with  the  rsdiui  of  the  orank,  it  wQI  In-  easily  nn- 

!.  that  within  certain  i  lltoT  the  time  when  the 

■  ■  port,  and  an 
in  vary  the  d 
I      traa  41  and  19  sho*  that  the  rod  of  the  valve  ii  attached  to 

it  by  a  T  joint,  which  leaves  the  valve  sufficiently  free  for  \> 

it  constant]]  i  hoe;  and  a  similar 

adjustment  is  adopted  with  the  distribution  valve. 

:ii..ns  w lii.  !i  we  have  given  in  tho  pn 
to  the  construction  and  notion  of  thisi 
evidently  appl]  to  other  systems,  which  merely  differ  in  some  of 
the  srrangementa  and  forma  of  the  compom  at  pk  •■•  a     Iforeow  r, 

in  <>iir  n  Hi  vvill  find  the  rules  and  tables  coin-erne.! 

in  Ihe  eslenlationa  and  designs  of  these  engines, 


aUl  BS   \M»  PRACTICAL  DATA 
BTJ 

l.ovv-.ri.  -v  u  vi . 

118.    In    'li- 
ra i-   prodnoad  at   n   tamparatore  very  lillle  over   that   of 

boding  wat.r.  or  100   i  I     iisuheit)    M  la, m  fast, 


BOOK   OF    INDUSTRIAL  DESIGN. 


generally  105°  cent.— in  which  case  the  tension  of  the  steam  will 
sustain  a  column  of  mercury  of  90  centimetres  in  height ;  that  is  to 
say,  14  centimetres  above  that  due  to  atmospheric  pressure.  It  is, 
consequently,  equal  to  a  pressure  of  117  atmospheres,  or  1-2  kilog. 
per  square  centimetre.  It  is  for  this  pressure  that  what  are  gene- 
rally known  as  Watt's  engines,  without  cut-off  valves,  are  calculated; 
and  the  one  we  have  been  examining  is  regulated  upon  this  datum. 

There  is,  however,  a  great  difference  between  the  pressure  of 
the  steam  in  the  boiler,  and  that  to  which  the  effective  power  of  the 
machine  is  due.  It  is  evident  that  a  part  of  the  pressure  will  be 
absorbed  by  the  back  pressure  due  to  an  imperfect  vacuum,  as  well 
as  by  the  friction  of  the  piston,  and  other  moving  parts,  aud  the 
leakage  and  condensation  in  the  steam  passages.  So  that,  taking 
into  consideration  these  various  causes  of  loss,  the  effective  force 
may  be  estimated  at  -5  kilog.  only,  per  square  centimetre,  in  the 
majority  of  engines,  whilst  it  may  reach,  perhaps,  -65  kilog.  in  the 
most  efficient. 

The  rule  for  calculating  the  power  of  low-pressure  steam-engines 
consists  in — - 

Multiplying  the  mean  effective  -pressure  of  the  steam  upon  the  piston 
by  the  area  of  the  latter,  expressed  in  square  centimetres,  and  the  pro- 
duct by  the  velocity  in  metres  per  second. 

The  result  of  this  calculation  will  be  the  useful  effect  of  the 
eno-ine  in  kilogrammetres. 

To  obtain  the  horses  power,  this  result  must  be  divided  by  75. 


Thus,  the  diameter  of  the  cylinder  of  a  low-pressure  non-expan- 
sive  steam-engine  being  -856,  and  its  section  5755  square  centi- 
metres, if  the  effective  pressure  upon  the  piston  is  -63  kilog.  per 
square  centimetre,  and  the  velocity  1-1076 — 

We  have 

•63  x  5755  x   11076  =  401567  k.  m. 
^Whence— 

4015-67  -=-  75  =  53-54  II.  P. 

But  the  effective  pressure  upon  the  piston  is  not  always  -63 
kilog.  per  square  centimetre ;  it  is  more  frequently  below  than  above 
this  amount.  It  varies  not  only  according  to  the  power  of  the 
machine,  but  also  according  to  the  state  of  repair.  Thus,  some- 
times the  effective  pressure  will  not  be  more  than  -45  kilog.  in 
small  engines,  whilst  in  large,  powerful  ones,  it  may  at  times  reach 
•65  kilog. 

Single-acting  engines,  such  as  are  employed  in  mines,  are  of  the 
same  dimensions  as  double-acting  ones,  but  of  only  half  the  power. 
Thus,  the  cylinder  of  a  low-pressure  steam-engine,  of  50  horses 
power,  and  only  single-acting— that  is  to  say,  receiving  the  action 
of  the  steam  during  the  descent  only  of  the  piston — is  exactly  the 
same  as  in  a  machine  of  100  horses  power,  in  which  the  steam  acts 
alternately  on  both  sides  of  the  piston. 

In  the  following  table,  which  applies  to  this  kind  of  steam-engine, 
we  have  given  the  diameters  and  velocities  of  the  steam-piston 
from  1  to  200  horses  power. 


TABLE  OF  DIAMETERS,  AREAS,  AND  VELOCITIES  OF  PISTONS,  IN  LOW-PRESSURE  DOUBLE-ACTING  STEAM-ENGINES,  WITH 
THE  QUANTITIES  OF  STEAM  EXPENDED  PER  HORSE  POWER. 


Diameter 

of 

piston. 

Area  of  Piston. 

Length  of 

Number 
vf 

revolutions. 

Velocity  of 
piston 

Velocity  of 

piston 
per  minute. 

Effective 
I  lie  piston 

per  square 

Weigh!  .if 

power. 

Total. 

Per 
horse  power. 

lower  per  lioui 

1 

2 

4 

6 

8 

10 

12 

16 

20 

24 

30 

40 

50 

60 

70 

80 

90 

100 

120 

160 

200 

15 
•21 
■30 
•35 
■40 
■45 
•49 
•55 
•61 
•66 
•73 
•83 
■91 
1-00 
1-07 
114 
1-21 
1-27 
1-39 
1-60 
1-78 

sq.  m. 
■018 
■036 
■068 
■098 
■128 
•159 
•189 
•240 
•292 
•346 
•414 
■535 
■658 
■779 
•903 
1032 
T138 
1-264 
1512 
2-005 
2-480 

sq.  cent. 
•181 
■178 
•171 
•163 
•160 
•159 
•157 
•150 
•146 
•144 
•137 
•134 
•132 
•130 
•129 
•W'i 
•126 
•126 
•126 
•125 
•124 

•52 
■61 
•76 
•91 
1-07 
1-22 
1-22 
1-37 
1-52 
1-69 
1-83 
1-99 
213 
2-28 
2-44 
2-44 
2-59 
2-59 
2-74 
3-00 
3-00 

50 
42 
34 
31 

27 
24 
24 

20 
18 
17 
16 
15 
14 
13 
13 
12 
12 
11 
10 
10 

•85 
•86 
•90 
•94 
•96 
•98 
•98 
1-01 
1-02 
1-02 
1-04 
1-06 
1-07 
1-07 
1-06 
1-06 
1-04 
1-04 
1-00 
1-00 
1-00 

51 
52 
54 
57 
58 
59 
59 
60 
61 
61 
62 
64 
64 
64 
63 
63 
62 
62 
60 
60 
60 

kilog. 
•49 
•49 
■49 
•49 
•49 
•49 
•49 
•50 
•51 
•52 
■53 
•53 
•54 
54 
•55 
•56 
•57 
■58 
•59 
■60 
•61 

kilog. 

38-81 
38-77 
38-77 
38-72 
38-72 
38-64 
3864 
37-80 
37-38 
36-88 
36-04 
35-70 
35-32 
34-94 
34-30 
3431 
3301 
32-97 
31-92 
31-67 
31-47 

. 

DIAMETER    OF    THE    PISTON. 

By  means  of  the  above  table,  we  can,  in  a  very  simple  manner, 
determine  the  diameter  and  velocity  of  the  piston  of  a  low-pressure 


double-acting  steam-engine,  supposing  the  steam  to  be  of  the 
pressure  of  1-17  atmospheres  in  the  boiler,  corresponding  to  a 
column  of  mercury  of  90  eentimAtws  in  height. 


-Up  lhc  att«  • 

of  th«-  c.-iw  l«>  be  <■•  n«lru.  '■ 
*  ..f  |...l«.o. 

f  a  low. 
pnwor>  .1   ubl* -arux.g  aUam-eogio*  of  25  horses  p 

In  i(,.  IheJ  the  ana 

■ 
bona  |  -  '"•  1"  r 

•    for  tho  total 

\  '    ■ ;        GT 

Thus,  tii--  dun 

;riE». 
and  per  minute,  given  in  the 
andu,1  erally  adopted  ae 

Um  rr_-  la    and    Inanu;. 

number 

piston,  p«i  minute,  for 

tli.-  number  va  ■  '■  ll  >H 

. 
■ 
: ..  itter  (he 

oca  the  height  of  the 
[uently,  mu.b  ihorter  for  the 
- 

rare  by 
■ 

make  a  few  .-  mioate 

iti«  i  lui.i  Bowd 

I  .  work 

i  of  (be 

i  tin'  ri-'jiiiri-.l  power. 

mil  by  «  very 

■ 

proper- 

1    :    I'M  111-, 

uiil 

t  phi 


-  uditure   |nr   :  r  hour. 

i  •  -  the  expeajas- 

i  araall 
a.  rt'ul  0O«a — tbf  reason  of  « 

I  I J  boraea  power,  th,e  ezpenditore  of* 
■  r   per  h'-ur  :  wtulat   for  an 
the  expenditure  on!;. 
for  a  like  power  in  tl.- 

bta  of  the  steam  have  been  ea 
from  tli.   |  uila: — 

W        A  x  S  x  to  x  3  N  x  60. 
•rw  power  j 

u>,  the  weight  of  a  cubic  metre  of  steam  at  the  pressure  en.; 
N,  the  Dumber  ol 

■  .1  not  ban  I  leiatkm  the  una  of  -• 

from  leakage  and  onnrtonaatlon  in  the  steam  ] 

passages,  w  hi.  h  i-  generally  estimated  at  one  tenth  of  Um 
expenditure,  aa  thia  Item  should  evidently  enter  into  the  caleula- 
ipecting  the  boiler. 

BTxaavnna  ami  ta- 
Tho  section  of  the  pipe  which  conveys  the  steam  to  the  i 

as  w.  II  aa  that  of  the  iniro.i.- 

■  the  piston. 
Wh.  ■  ii.it  the  diameter  of  the  steam-pip- 

Bfth  of  that  of  the  ej 
Wo  i  remark,  that  tl  •  of  the 

■ 
of  thia  that,  in  locomotive  ■ 
:i  i-  somatii  nth  or  a  ninth  of  th.it  of  the 

cylinder,  ma  time  (be  preaaure  of  thi 

more,  in 

AIK-I'I'MP    AM 

The  stroke  of  the  air-pun  I  of  the 

be  saine  number  of  strokes. 
•  a  quantity  ol 
■ 

l>  in. ;  and  the 

- 
ibic  in.,  it  followa  that  the  pump  ■  J  a  littlo 

more  ;!.  I  the  volume  ••«  ut  oul  bj  tin 

of    lie- 
angina. 

1    ar.a   of  tie  !  of  the 

pump,  and  in  length  ia  abonl  :yis,at 

•  r  \  ari.  * 
.   vv.it.  r.  it   will   be  Well 
to  know  bow  I 

To  i;.  I  uswaf : — 


BOOK  OF    INDUSTRIAL  DESIGN. 


Rule. — Take  the  excess  of  the  temperature  of  the  steam  over  that 
of  the  injected  water,  and,  after  adding  550  to  it,  multiply  it  by  the 
weight  of  sltam  to  be  condensed,  and  divide  the  product  by  the  differ- 
ence of  temperature  between  (lie  discharged  and  the  injected  water. 
The  quotient  will  be  the  weight  of  cold  water  to  be  injected. 

Thus,  let  w  represent  the  weight  of  the  steam  to  be  condensed; 
/,  its  temperature ;  W,  the  weight  of  the  cold  water  to  be  injected 
into  the  condenser ;  t',  its  temperature ;  and  T,  that  of  the  water 
discharged : — 

We  have 

w  (550  +  *  —  T) 


W 


If  we  make  w 
we  shall  have 


W  = 


T  —  t' 
16,  V  —  12°  cent.,  T  =  38°,  and  t  —  105°, 

26-16(550  +  105"  — 38°) 


38°  —  12° 

Whence,  W  =;  621  kilog.  or  litres,  for  the  expenditure  per 
minute  of  cold  water  in  the  condenser. 

That  is  to  say,  the  quantity  of  water  to  be  injected  into  the  con- 
denser should,  in  this  case,  be  about  24  times  the  weight  of  the 
steam  expended. 

If  the  discharged  water  were  of  the  temperature  of  55°,  the  cold 
water  remaining  at  12° — 

We  should  then  have 

26-16(550+  105°  — 55°) 
55°  — 12° 
Whence — 

W  =  365  kilog.  or  litres. 

That  is  to  say,  that  in  the  last  case  the  water  injected  would  not 
be  more  than  14  times  the  steam  expended. 

But  it  is  to  be  remarked,  that  in  this  case  the  force  of  the  steam 
in  the  condenser,  at  a  temperature  of  55°,  is  equal  to  a  column  of 
mercury  of  12-75  centimetres  in  height;  whilst,  in  the  first  case,  it 
would  only  be  equal  to  a  column  of  5-5  cent.  There  is,  therefore, 
an  advantage  in  employing  sufficient  injection-water  to  produce  the 
lower  of  the  two  temperatures. 

From  the  preceding  results,  we  may  deduce  what  follows  : — 

First,  That  the  stroke  of  the  air-pump  piston,  in  low-pressure 
double-acting  steam-engines,  is  ordinarily  equal  to  half  the  stroke 
of  the  steam-piston.  ^ 

Second,  That  the  diameter-of  the  air-pump  piston  is  equal  to 
about  two  thirds  of  the  diameter  of  the  steam  piston ;  and,  conse- 
quently, its  area  is  about  half  that  of  the  latter. 

Third,  That  the  effective  displacement  of  the  air-pump  piston — 
that  is,  the  cubic  contents  of  the  cylinder  generated  by  the  disc  of 
the  piston — is  equal  to  an  eighth,  or  at  least  a  ninth,  of  the  contents 
of  the  cylinder  generated  by  a  double  stroke  of  the  steam-piston. 

Fourth^  That  the  capacity  of  the  condenser  is  at  least  equal  to 
that  of  the  air-pump. 

Fifth,  That  the  sectional  area  of  the  passage  communicating 
between  the  condenser  and  air-pump  is  equal  to  one-fourtli  the  area 
of  its  piston. 

Sixth,  That  the  quantity  of  cold  water  to  be  injected  into  the 
condenser  varies  according  to  its  temperature,  and  to  the  tempera- 
ture of  the  water  discharged. 

Seventh,  That  this  quantity  is  equal  to  24  times  tht  weight  of 


steam  expended  by  the  cylinder,  where  the  mean  temperature  of 
the  cold  water  is  12°,  and  that  of  the  water  of  condensation  38°, 
which  are  generally  what  exist  in  low-pressure  double-acting 
engines. 


COLD-WATER   AND    FEED    PUMPa. 

The  capacity  of  the  cold-water  pump  should  be  the  24th  or  18th 
of  that  of  the  steam  cylinder.  The  capacity  of  the  feed  or  hot- 
water  pump  should  be  the  230th  or  240th,  at  least,  of  that  of  the 
steam  cylinder. 

HIGH-PRESSURE    EXPANSIVE    ENGINES. 

Let  the  following  dimensions  be  given  for  an  engine  analogous 
to  that  which  we  have  just  described : — 

Diameter  of  the  cylinder, =  -275  m. 

Stroke  of  the  piston, =  -680  m. 

Area  of  the  piston, =  -0594  square  m. 

Number  of  double  strokes  per  minute, =  -40 . 

Let  us  suppose,  in  the  first  place,  that  when  the  steam  reaches 
the  cylinder,  its  pressure  is  equal  to  5  atmospheres,  and  that  it  is 
cut  off  during  three-fourths  of  the  stroke  ;  that  is  to  say,  that  tho 
cylinder  only  receives  the  steam  during  the  first  quarter  of  the 
stroke. 

This  pressure  of  5  atmospheres  is  equal  to  5  x  1-033  =  5-165 
kilog.  per  square  centimetre.  Consequently,  the  total  pressure 
exerted  upon  the  surface  of  the  piston  is — 

5-165  x  594  sq.  cent.  =  3068  kilog. 

And  as  with  this  pressure  the  piston  passes  through  a  space 
equal  to  one-fourth  of  its  stroke,  or 

■680  -7-  4  =  -170  m., 
it  is  capable,  theoretically  speaking,  of  transmitting  an  amount  of 
force  expressed  by 

3068  x  -17  =  521-56  kilogiammetres. 

Next,  dividing  the  length,  -51  m.,  or  the  remaining  three-fourths 
of  the  stroke,  into  an  even  number  of  equal  parts — as  four,  for 
example — each  of  these  parts  will  be  equal  to 

—  =  -1275  m. 

4 

Now  we  know  that,  according  to  Mariotte'a  law,  the  successive 
volumes  of  a  given  quantity  of  any  gas  are  in  the  inverse  ratio  of 
their  tension  or  pressure,  provided  the  gas  is  in  the  samo  condition 
throughout.  This  principle  may  be  regarded  as  quite  true  in  steam- 
engines,  because  the  expansion  is  never  carried  very  far,  and  as  tho 
strain  passes  through  the  cylinder  with  great  rapidity,  and  is  con- 
tinually being  renewed,  after  a  certain  time  and  when  the  cylinder 
has  become  warm,  its  temperature  is  very  little  below  that  of  the 
steam  itself,  and  the  latter  suffers  no  appreciable  change  in  passing 
through  it.  Putting  P  for  the  pressure,  3068  kilog.,  as  found  for 
the  first  quarter  of  the  stroke,  we  may  state  the  relations  of  the 
volumes  and  pressures  in  the  following  manner;  that  is,  at  the 
points,  1,  2,  3,  4,  5,  of  the  stroke,  or  for  the  successive  spaces, 
•170  hi.,  -295  m.,  -425  m.,  -5525  m.,  -680  m. 


IM 


TV»  rurreapuadaaf  pwwii  will  be— 

- 
of  leaa*-, 

3068  a,       1761  k, 

■«««*t  to  Simpson'*  method,  wt  hare 

TV.  ...  WUWiiiimi  iihiiii,  •  -      »"»+   W7  »    *«» 

T-t~  U»  HMIIHIlUl^  i»uim  .'  tXl»=     MM 

r«f  iim  ta»  f  ■■-■~  «f  tW  «■»■  1(1*14+  M 

T«tal,  ITIil 

Taking  the  third  of  this  quantity,  and  multipl; 
re  ahall  have  the  work  pun  out  during  the  cut-otT.     Thus — 

=  727-64  k.  m. 

Adding  to  thi-i  621  56  k.  m.,  the  work  given  out  before  tin-  cut- 


off, we  •hall  have  ll  ■  i  by  the  ateam 

during  '  '»■  piaton — 

=  1241*2  k.  m. 
.  thia  the  effect  of  the  atmospheric  pressure, 
•    :i  throughout  the  stroke,  and 
.  il  equal  to 

Ik.   x  594  sq.  c  x  -68  m.  =  417  25  k.  m., 

;     ]),••   |,'|. t.  ill 

m., 
nearly,  ;  -  ;  and  as  th>    | 

per  minute,  th<-  effective  force  per  minute  becomes 
in. ;  tiiat  b,  56660  kili-grainiues,  raised  one 

-.  as  well  as  of  most  other  expansive 
■tsssavengines,  will  b*  obtaiaed  in  a  much  more  siru|>lc  and  leas 
-.  bj  taking  advantage  of  the  following  tab 


TABI.F.  OF  Tli:  Kll.'H;i:\MMiTi:i>.  GIVES  OUT  WITH  VARIOUS  1'D.l.:  a  il  BIO 

I    .  Al:l"l  -  1  .. 


Fore*  pTro  oat,  eurrcipaadiQf  with  thr  prewar*  of 

V4«a» 

l 

11 

1 

t| 

l 

4 

i 

6 

•  :i  sat), 

••      . ,  -i 

■1 

f  ■  q  i.. 

■H     BJ  '.. 

■tSMS]  Bi 

»!n.  •;  h. 

>■■     .    • 

•»t»c  M*lnm 

k.  si. 

k.  m. 

km. 

k.  m. 

k.   DJ. 

turn. 

turn. 

k.  m. 

41333 

• 

■ 

" 

84174 

1-71  t 

119978 

116819 

4 1 57  i 

194799 

54918 

. 

71976 

. 

1  17946 

6S9I9 

" 

1011  I" 

161710 

450 

- 

617 

. 

67410 

161784 

' 

111796 

167694 

43619 

1704  18 

79190 

7  11-7 

121764 

189646 

77010 

99  1 1 2 

193916 

• 

194616 

• 

94479 

96417 

■ 

81117 

97341 

1  ,|,  -j 

98941 

•"ill 

198338 

9-25 

9-50 

- 

l 

68254 

BOOK   OF   INDUSTRIAL   DESIGN. 


According  to  this  table,  if  we  have,  to  calculate  the  force  acting 
upon  the  piston  in  this  engine,  in  the  same  circumstances,  we  must, 
in  the  first  place,  ascertain  the  original  volume  of  the  steam  intro- 
duced into  the  cylinder  during  the  first  quarter  of  the  stroke  of  the 
piston.     This  volume  is  equal  to 

•0594  x  -17  =  -010098eubie  metres. 

Now  it  will  be  seen  from  the  table,  that  the  force  given  out  when 
a  cubic  metre  of  steam,  of  a  pressure  of  5  atmospheres,  expands  to 
four  times  its  original  volume,  is  equal  to 
123290  k.  m. 

Consequently,  that  corresponding  to  a  volume  of  -010098  cubic 
metres  will  be —  ■ 

123290  x  -010098  =  1245  k.  m., 

And  deducting  from  this  the  atmospheric  pressure,  which  resists 
the  motion  of  the  piston,  wo  have 

1245  —  417  =  828  k.  m., 
a  quantity  which  differs  very  little  from  that  obtained  by  the  more 
tedious  calculation.  Thus,  the  calculation  for  determining  the 
effective  power  of  a  steam-engine,  of  which  we  know  the  diameter 
and  stroke  of  the  piston,  the  pressure  of  the  steam,  and  the  amount 
of  cut-off,  reduces  itself  to  the  following  rule  : — 

Rule. — Multiply  the  area  of  the  piston  by  the  portion  of  the  length 
of  the  stroke,  during  which  the  steam  acts  with  full  pressure,  and  you 
will  determine  the  volume  of  steam  expended.  Multiply  this  volume 
by  the  amount  of  kilogrammetres  in  the  table,  corresponding  to  the 
pressure  of  the  steam  and  to  the  final  volume,  and  then  deduct  from 
the  product  the  amount,  in  kilogrammetres,  of  the  atmospheric  pressure 
opposed  to  the  piston  during  the  entire  stroke,  and  the  result  will  be 
the  theoretic  amount  of  force,  in  kilogrammetres,  given  out  by  the 
steam  during  a  single  stroke  of  the  piston. 

A   MEDIUM-PRESSUKE    CONDENSING   AND    EXPANSIVE    STEAM- 
ENGINE. 

Let  the- following  data  be  assumed  : — 

The  diameter  of  the  steam-cylinder  =  -330  m. 

The  stroke  of  the  piston =  -650  m. 

The  diameter  of  the  air-pump =  -180  m. 

The  stroke  of  its  piston =  -325  m. 

The  diameter  of  the  feed-pump . . . .  =  -035  m. 
The  stroke  of  its  plunger =  -235  m. 

It  follows,  from  these  dimensions,  that  we  shall  have — 

The  area  of  the  steam-piston =  855-30  sq.  cent. 

The  area  of  the  air-pump  piston  . . .  =  254-47        " 
The  area  of  the  feed-pump =      9.62        " 

And  for  the  displacement,  or  volumes  of  the  cylinders  generated 
by  the  pistons — 

That  of  the  steam  cylinder . .  . .  =  55-594  cubic  decim. 

That  of  the  air-pump =    8-270         " 

That  of  the  feed-pump =      -226        " 

We  shall  suppose  that,  when  the  engine  is  in  regular  working 
condition,  the  pressure  of  tho  steam  is  31  atmospheres;  and  we 
must  ascertain  what  is  the  actual  force  given  out,  supposing  the 
steam  to  be  cut  off  during  three-fourths  of  the  stroke  of  the  piston. 


That  is  to  say,  that  the  steam  is  admitted  into  the  cylinder  only 
during  a  quarter  of  the  stroke,  which  corresponds  to  -1G25  m. 

Since  the  sectional  area  of  the  cylinder  is  -0885  m.,  the  volnmo 
of  steam  expended  during  a  fourth  of  the  stroke  will  be  equal  to 
•0885  x  -1G25  =  -0139  cubic  metres;  or, 
13-9  cubic  decimetres. 

Now,  according  to  the  table  of  the  amounts  of  force  given  out  by 
the  steam  at  various  pressures,  it  will  be  found  that  the  force  due 
to  a  cubic  metre  of  steam,  of  an  initial  pressure  of  3j  atmospheres, 
when  allowed  to  expand  to  four  times  its  volume,  is  equal  to  8G303 
kilogrammetres.  As  the  table  does  not  give  the  actual  amount  foi 
3|  atmospheres,  it  may  be  taken  by  adding  together  that  for  2'2 
and  1  atmospheres.     Thus — 

61645  +  24658  =  86303  k.  m. 

We  have,  therefore,  in  the  present  case — • 

■0139  x  86303  =  11996  k.  m., 
as  tho  force  due  to  a  single  stroke  of  the  piston. 

From  this  quantity,  however,  .we  must  deduct  the  back  pressure 
due  to  the  imperfect  vacuum  in  the  condenser.  This  back  pressure 
is,  in  the  generality  of  cases,  equal  to  about  -27  kilog.  per  square 
centimetre,  when  the  temperature  of  the  water  of  condensation  is 
about  65°  cent. 

Allowing  this  to  be  the  case  in  the  present  example,  we  shall 
have  to  deduct  from  the  preceding  result  the  action  of  this  back 
pressure  upon  tho  whole  surface  of  the  piston,  and  during  the  entire 
stroke.     This  is 

■27  x  -0885  x  -65  x  150-1  k.  m., 

We  have,  consequently, 

,1199-6  —  150-1  =  1049-5  k.  m., 
for  the  actual  force  given  out  by  the  piston  during  a  single  stroke ; 
and  if  this  engine  works  at  the  rate  of  42  revolutions  per  minute, 
which  supposes  the  velocity  of  the  piston  to  be  -9  m.  per  second, 
wo  shall  find  that  the  mechanical  effect  per  minute  will  be  equal  to 
1049-5  x  84  =  981588  k.  in  ;  or, 
881598  -f-  4500  =  1959  horses  power. 

It  is  well  known,  however,  that  this  amount  is  far  from  being  all 
transmitted  by  the  first-motion  shaft,  for  a  portion  is  absorbed  in 
overcoming  the  friction  of  the  various  moving  parts  of  the  engine, 
and  there  are  also  other  causes  of  loss. 

If  we  reckon  that  the  force  which  is  really  utilised  is  not  more 
than  four-tenths  of  that  theoretically  due  to  the  steam,  in  which 
case  we  must  suppose  that  six-tenths  are  completely  lost,  we  shall 
have  for  the  effective  force  transmitted  to  the  first-motion  shaft— 

19-59  x  -4  =  7-84  horses  power; 
or  almost  8  horses  power,  of  75  kilogrammetres  each. 

If  it  is  desired  to  know  the  quantity  of  fuel  consumed  per  hour 
in  producing  this  mechanical  effect,  we  may  remark,  that  a  cubic 
metre  of  steam,  at  a  pressure  equal  to  3  J  atmospheres,  weighs  1  -85 1 8 
kilog. ;  and  at  a  pressure  of  4  atmospheres,  it  weighs  2-0291  kilog. 

Now,  although  we  have  supposed  the  pressure  in  the  cylinder  to 
be  3|  atmospheres,  we,  nevertheless,  allow  that  it  will  be  conside- 
rably more  in  the  boiler,  to  cdrnpensate  for  the  leakage  in  the  valve- 
easing,  passages,  and  valves. 

Taking  4  atmospheres  as  the  pressure  in  the  boiler,  it  will  be 
found  that  the  weight  of  steam  expended  for  each  single  stroke  of 
the  piston  is — 


hit:   rn.v  : 


•oi»  x  9<*i  =  -©»i  i 

•Atl  prr  • 

I  kflofl. 

Frwn 

....  that  Uio  quantity     I 

I  ;• .  <  1    .    <;  ■  h"ur. 


Ad<1  • 
\\ 

Jill  -4-  7-84  =  3  1 

-.  pa?  li.nir. 
npleto  the  r  en,  we  add  u. 

- 
of  dilVcrriit  kinds: — 


.      \\l  I  M.IN  M>  WITH   oil 

i   ATMOSPHERES  I.N  TUJ  >D  Al' 


'■ 

Su..k. 

»i  i-.'.^. 

• 

rotlmj  off 

•Irak*. 

nj  ulT  ti  uatvfuunh. 

p.l^O. 

I-T  K«  H.J. 

•■*'  ■■"""•• 

_. 

1 

■ 

i-' 

■ 

,.i.:..u. 

hiTW     uiiwcr. 

■ 

Ml 

ML 

■q.  mil. 

kii  «. 

-\    rrnU 

cent. 

Ular. 

1 

10 

94-90 

1 1 

1 18 

10 

so 

too 

19 

i   6 

l  1 

I 

1  IS 

194 

18 

SI 

198 

•ji 

8 

337 

1J7 

38 

11  '. 

- 

31-7 

' 

119 

91-36 

IJ 

BO-0 

41 

li  j 

91-18 

38 

SO 

110 

28-6 

■I.. 

mi 

19 

*7 

190 

no 

hi 

10 

81 

81 

64 

99 

49 

78 

84 

ISO 

rn 

69 

79 

69 

71 

18-64 

68 

38 

-  ■ 

67 

•  i 

170 

70 

17-98 

69 

43 

1  10 

7J 

68 

17-99 

66 

58 

sa  g 

87 

17-10 

7J 

.,i 

60 

16  ■ 

85 

67 

16-69 

84 

66 

66 

rABLK   OF    PROPORTIONS    OP    MEDIUM    l  ^  IT  11    TWO 

CYLINDERS    OH    WOO}  '■  -    BYSTJ  M;    PBJ 


>r*  in 

Arei  of  jnitoni  id  square  centimctroi. 

Stroke  of  puloni  in  n>.  1 

4. 

D 

IVr  ltor»-  j*i*rr. 

t. 

I 

a. 

A. 

" 

A. 

4 

I«, 

60 

l  i  : 

■90 

|i 

■ 

17 

160 

■67 

•:mi 

91 

1  184 

1  II 

-  1 

i  i  i 

300 

416 

II 

188 

IJ 

46 

491 

40 

■89 

1-10 

97-a 

16 

816 

•J  1 .'  1 

88 

i    . 

1-90 

9990 

n  i 

■''7 

1-80 

• 

33 

118 

1-30 

8117 

80 

108 

91-6 

1076 

98 

1-Jil 

1-80 

•Jl  <i 

'- 

96 

88 

1-97 

i  70 

89-1 

71 

1  194 

>7 

1-97 

1  7(1 

L'J  1 

41 

ins 

I  B0 

l£«i 

i     ■ 

■ 

26 

34 

i     ' 

51 

3048 

-i 

i  60 

i  VI 

•j  in 

18*0 

104 

1  .7 

9-10 

1-  8 

110 

84 

i  67 

I  i" 

i-  B 

II  1 

B019 

1-67 

9-10 

05 

118 

84 

i   .: 

•J  in 

18-6 

BOOK   OF   INDUSTRIAL  DESIGN. 


CONICAL    PENDULUM,   OR    CENTRIFUGAL    GOVERNOR. 

The  centrifugal  ball-governor  is  compared,  in  physics,  to  a 
simple  pendulum,  the  length  of  which  is  equal  to  the  distance  of 
the  point  of  suspension  from  the  horizontal  plane  passing  through 
the  centres  of  the  balls ;  and  the  duration  of  an  entire  revolution  of 
the  ball-governor  is  equal  to  that  of  a  completo  oscillation  of  the 
pendulum. 

The  formula  for  determining  the  vertical  height  or  the  distance 
of  the  point  of  suspension  above  the  plane  of  the  balls  is,  conse- 
quently, the  same  as  that  employed  to  find  the  width  of  a  pendu- 
lum, of  which  we  know  the  number  of  oscillations.  It  may  be 
reduced  to  the  following  rule: — 

Rule. — Divide  the  constant  number,  89,478,  by  the  square  of  the 
number  of  revolutions  per  minute.  The  quotient  will  give  the  height 
in  centimetres. 

Example. — What  is  the  vertical  height  or  distance  of  the  point 
of  attachment,  from  the  horizontal  plane  passing  through  the 
centres  of  the  balls  of  a  governor,  revolving  at  the  rate  of  40  turns 
per  minute? 

We  have  40s  =  1600, 

and  89478  -4-  1600  =  56  centimetres, 

for  the  height  sought. 

With  this  rule,  it  will  be  easy  for  us  to  calculate  the  heights  of 
conical  pendulums,  from  the  velocity  of  25  revolutions  per  minute, 
to  that  of  67 ;  and  within  these  will  be  found  the  rates  of  combi- 
nations more  generally  met  with  iu  practice.  We  have  given 
them  in  the  following  table,  adding  a  column,  which  gives  the 
difference  iu  height  for  each  revolution.  And  as  the  angle  which 
the  arms  of  the  governor  make  with  the  spindle  is  generally  one 
of  30°,  when  the  balls  are  in  a  state  of  repose,  or  are  going  at 
their  minimum  velocity,  we  have  given,  iu  the  fifth  column  of  the 
table,  the  lengths  of  these  arms,  from  their  point  of  suspension  to 
the  centres  of  the  balls,  assuming  the  angle  of  30°,  and  making 
them  to  correspond  with  the  number  of  revolutions  given  in  the 
first  column. 

In  calculating  the  lengths  of  the  arms,  we  have  employed  the 
following  practical  rule : — 

Rule. — Divide  the  cdnstant  number,  103,320,  by  the  square  of  the 
number  of  revolutions  per  minute,  and  the  quotient  will  be  the  length 
in  centimetres. 

Example. — Assuming  the  angle  to  be  30°,  what  should  be  the 
length  of  the  arms  of  a  conical  pendulum,  making  37  revolutions 
per  minute? 

We  have  3V  =  1369. 

mi.  10-3320 

Then—  ■  ,^»    =  75'46  centimetres, 

13o9 

for  the  length  of  the  arms  of  the  pendulum,  or  the  diameter  of  the 

circle  described  by  the  balls. 

It  is  evident,  that  if,  on  the  other  hand,  the  length  of  the  arms, 
with  this  angle  of  30°,  is  known,  the  number  of  revolutions  which 
the  balls  make  in  a  minute,  will  be  found  by  dividing  the  number, 
103,320,  by  the  length  of  the  arms  expressed  in  centimetres,  and  then 
extracting  the  square  root  of  the  quotient. 

The  weight  of  the  balls,  according  to  the  resistance  they  have 
to  encounter,  is  as  important  to  determine  as  the  length  of  the 


suspending-arms,  in  order  that  the  governing  action  of  the  pendu- 
lum may  be  sufficiently  powerful  and  quick.  It  often  happens,  in 
badly  designed  engines,  that  the  governor  produces  no  effect,  be- 
cause, the  length  of  the  suspending-arms  is  not  proportionate  to 
the  velocity,  or  because  the  weight  of  the  balls  is  not  proportionate 
to  the  resistance  to.be  overcome. 

We  have  considered  that  it  would  be  a  great  convenience  to 
engineers  and  artisans  to  possess  a  table,  showing  at  sight  the  ve- 
locities and  corresponding  lengths,  for  the  conical  pendulums,  or 
ball-governors,  generally  employed  in  steam-engines,  so  as  to 
enable  them  to  determine  with  certainty  the  exact  proportions  to 
be  given  thotn,  in  relation  to  their  spindles  and  driving-gear. 
When  these  points  are  determined,  the  weights  of  the  balls  may  be 
easily  adjusted. 

TABLE  RELATIVE  TO  THE  DIMENSIONS  OF  THE  ARMS  AND  TO  THE 
VELOCITIES  OF  THE  BALLS  OF  THE  CONICAL  PENDULUM  OR 
CENTRIFUGAL   GOVERNOR. 


Number  of 
Revolutions 
per  Minute. 

Square  of  the 
Velocities. 

Length  of 
Pendulum  in 
CentimetreR. 

Difference  of 

Length  for  one 

Revolution. 

Length  of  Amu 

with  an  Angle 

of  3u°. 

Cent. 

Milt. 

Cent. 

25 

625 

143-1 

108 

16 

26 

676 

132-4 

96 

153 

27 

729 

122-7 

86 

142 

28 

784 

114-1 

77 

132 

29 

841 

106-4 

70 

123 

SO 

900 

99-4 

63 

116 

31 

961 

93-1 

57 

107 

32 

1024 

87-3 

52 

101 

33 

1089 

82-1 

48 

95 

34 

1156 

77-4 

44 

89 

35 

1225 

73-0 

40 

84 

36 

1296 

69-0 

37 

80 

37 

1 369 

65-3 

34 

75 

38 

1414 

61-9 

31 

71 

39 

1521 

58-8 

29 

68 

40 

1600 

55-9 

27 

64 

41 

1681 

53-2 

25 

61 

42 

17  64 

50-7 

23 

68 

43 

1849 

48'4 

22    ■ 

56 

44 

1936 

46-2 

20 

63 

45 

2025 

44-2 

19 

51 

46 

2116 

42-3 

18 

4 'J 

47 

2209 

40-5 

17 

47 

48 

2304 

38-8 

16 

45 

49 

2401 

37-3 

15 

43 

50 

2500 

35-8 

14 

41 

51 

2601 

34-4 

13 

40 

52 

27n4 

33-1 

12 

38 

53 

2809 

31-8 

12 

37 

54 

2916 

30-7 

11 

33 

55 

3025 

29-6 

10 

34 

56 

813B 

28-5 

10 

35 

57 

3249 

27-5 

9 

32 

58 

3364 

26-6 

9 

3) 

59 

3481 

25-7 

8 

30 

60 

3600 

24-8 

8 

29 

61 

3721 

24-8 

8 

28 

62 

:;s44 

23-3 

7 

27 

63 

3969 

22-5 

7- 

26 

64 

4096 

21-9 

7 

25 

65 

4225 

21-2 

6 

24 

66 

4356 

20-5 

6 

24 

67 

4489 

19-9 

6 

'  23 

68 

4624 

19-3 

23. 

Note. — With  an  angle  of  30°,  the  centrifugal  force  is  the  same  for 
all  lengths  of  pendulum. 

This  table  may  also  be  consulted  in  the  case  of  single-armed  pendu- 
lums, which  are  occasionally  employed,  instead  of  centrifugal  gover- 


the  rn  actical  it.  \>  <:iir 


CHAPTER  XI. 

OBLIQD  i:    PROJ  EJ3TI0 

AmxATta*  or  iruf  10  thi  deliseatios  or  ah  oscillatisi;  stiam  <  vi-isdes. 
II    \TK    M.I. 


tr>-»i  drawing,  (he  plane*  ..  o  which 

the  ob.    '  M  to  be 

|nr»:'.     '  which  it  folio 

:  the  machine  it 

»;■!«.•»• 

thai  til  cannot  Ik-  |«imllrl  to  II  planes. 

ju.ntly, 

■  vidently  appli- 
li  i-.,  however, 

l   parallel  tn  t1- 
portions  and  ilinif  n- 

•    the  production  of  tlm  oblique 

- 

■  both  the  liori- 

nt  this  nut.  in  Bg.  i.  as  placed  with  ita  base 
parallel  to  an  auxiliary  horizontal  pit  I  .1  bj  the  due, 

.;  /.  C  </  t  f. 

■  make  the  vertical  projection  of  this  j>ri- • ; 
I'lano,  parallel  to  one  of  the  fact  i.  nr  t.i  a  <l.  we  should,  in 
bare  the   projection  of  the  edgi  a, 

he  lii f  inb : 

In  iii.ii  aotaal  position 

the  nut ;  and  it  is,  therefore,  tin-  base  Une  of  the  two 

I  is,  we  shall  suppose,  the  angle,  i.  <>  i.', 

*itii  tin.  base  line  nf  tin-  actual  drawing  in  hand,  which  angle, 

amount  of  inclination  of  the  top  ami  bottom 

prism,  with  the  actual  horizontal  plane;  whilet  the  angle, 

■  mod  by  the  perpendiculars,  drawn  tn  each  of  the  lines 

amount  nf  inclination  of  tin' 

of  tin-  prism  with  regard  to  the  vertical  plane.   After 

nr.liT  In  nb'ain   III.'  [mints,  ,l',h\r\it, 

nd  Lit  of  tin-  point,  -.,  on  the  line,  t.'  t',  the 
i  ./...mi.  I  b  g  or  eg,  derived  Iron  li^'.  I.     D 
nlara  tn  tin.  Una,  l't",  through  each  of  the  points,  .i'.V,.  ■'../', 
»n«l  limiting  them  by  tin-  In.  -,  ,1'  ,ft  an. I  a* ./\  Bg,  •_'.  parallel  tn  Ihe 

upon  the  ainiiinry  ptane,  parallel  to  one  of  tin  Winn 

-  ■■!  ii..-  urn  brouided,  or  terminated  by  s  - 

.-  already  seen  (186),  Ita  eqn- 

tmir  Is 

if  tin.  two  projeotioni 

*  :  ...  I.   1  ; 

fig.  1  giving  the  widths,  tin-  distances  of  each  of  the  poinl 


1  lino,  a  ,/,  whk                      Dgfa  tin.  centre,  o,  :. 
defining  tin-  *•  -  ■  ■(  tin-  varl 

the  horizontal  plane, 
'I'..  this  in. I,  through  snj 

;  tin-  horizontal  |ir..j.  1 1 
line,  and  througb  tin-  correapondin(  '  Bg.  :!.  draw  a 

conple  nf  horizontal  linos,  cutting  ii  The 

Deration  is  performed  with  regard  to  ,l,\r, 

which  an-  projected  in  /-  ,  •  i.    Tne  wholi 

consists,  therefore,  in  drawing  vertical  linos  through  each  of  tlm 

i'i  ii;;.  1,  ami  horizontal  lines  through  Ihe  corresponding 
points  in  Bg.  -.     Tin  intersections  of  tin 
tions  of  tin-  extremities  of  each  ..t  tin-  •  Igea  in  tin-  oblique  view, 

If  it  is  wished  tn  obtain  t!  ■  if  tin-  eirculai 

with  minute  exactness,  it  will  :  to  determine,  s 

three  points  in  each  an-:  and  as  we  have  the  extremities  already, 
we  ..ill)  require  now  to  find  tin-  middle  of  each.    It  i»  tin 
tin-  circle  representing  tin-  central  opening  nf  tin-  nut.    It*,  oblique 
projection  Men  are 

obtained  by  tin'  projection  nf  the  two  diameters  perpendiculsr  to 
inn-  another,  one  of  which,  m  n,  is  parallel  to  the  vertical  pis 

lalter  In  magni  uently,  giving  tin-  tranavemo 

axis  of  the  ellipse,  while)  Ihe  other  is  inclined  ami  foreshortened, 

■    :i\is. 

431.  In  general,  tin-  oblique  projection  of  any  circle  is  always  an 
ellipse,  tin'  transverse  axis  nf  which  is  equal  tn  tin'  actual  diameter 
of  tin-  I'iivli'.  whilst  tin-  conjugate  .i\is  is  variable,  according  tn  the 
Inclination  or  angle  which  the  plane  nf  tin'  circle  makes  with  one 
of  the  pi  '"ii.    The  application  of  this  principle  will 

b  The  two  fust  nf  tins,-  figures  ropro- 

s.  iii  ii..-  horizontal  ami  vertical  projections  made  upon  the  auxiliary 
plains  i. fa  portion  of  the  cylindrical  rod,  a,  nf  tin-  piston,  n.  w..rk- 
ing  in  tin-  oscillating  steam-cylinder,  c;  ami  the  last.  fig.  ".  is  tlm 
oblique  projection  nf  this  part  nf  tin-  piston-rod  npon  lbs  vertical 
Tin:.'  tn  that  <i(  tlm  drawing. 

It  will  In-  remarked,  that  tin-  upper  part  nf  the  fragment  nf  the 
r- ■■  1  being  limited  by  a  plan.-.  /.  /,  perpendicular  tn  its  axis, 
i  'lips..,  tin-  transversa  axis,/. ./.  nf  which  is  ■ 
A  /,  whll  axis.  /'/,',  is  equal  tn  tlm  projection  •■!  this 

line,  A  /.  i.n  liur.  ".    Tlm  cylindrical  fillets,  r  .«,  i  u,  dtc,  nf  (his  rod, 
an-  projected  obliquely,  as  similar  ellipses,  of  whi  I 
ere  apparent     For  tlm  tome,  or  ring,  which  is  comprised  i 

the*)  two  fillets,  tl blique  projection  is  a  curve,  which  results 

from  tlm  Intersection  nf  an  elliptical  cylindi  i 

which  are  horizontal,  ami  tangent  tn  tin-  external  surf; f  tlm 

turns.    If,  ih.  i.  ]..  determine  this  eurve  witti 

n,  we  must  use  the  verj  same  method  adopted  in  determining 
the  shadow  propel  of  tlm  external  surface  nf  the  ■■  i 


BOOK   OF    INDUSTRIAL   DESIGN. 


155 


practice,  however,  when  the  drawing  is  on  but  a  small  scale,  we 
may  content  ourselves  with  determining  the  principal  points  in  the 
curve,  by  projecting  first  the  point,  v,  situated  upon  the  middle  of 
tne  diameter,  y  y,  of  the  torus,  and  drawing  through  it  the  line, 
v1  v\  equal  to  the  diameter ;  and,  secondly,  drawing  the  horizontal 
lines  touching  the  external  contour  of  the  torus  in  the  points,  z,  z', 
fig.  6,  over  to  za,  z3,  upon  the  axial  line,  I'  o',  fig.  7 ;  then  draw  an 
ellipse  with  these  two  lines,  v1  v*  and  zJ  za,  for  the  transverse  and 
conjugate  axes  respectively.  The  key,  D,  which  passes  through 
the  rod,  a,  being  rectangular  in  section,  is  projected  in  fig.  7,  by 
a  couple  of  rectangles,  as  indicated  by  the  dotted  projection  lines. 

422.  Proceeding  upon  these  principles,  we  can  make  obliquo 
projections,  in  a  very  simple  manner,  of  various  objects,  more  or 
less  complicated  in  form,  when  we  have  already  the  projections  of 
these  objects  upon  auxiliary  planes,  making  any  known  angle  with 
the  actual  plane  of  the  drawing.  Thus,  figs.  10  and  13  are  the 
oblique  projections  of  an  oscillating  steam-cylinder,  the  first  repre- 
senting the  cylinder  in  external  elevation,  whilst  the  second  is  a 
section  made  through  the  axis  of  the  cylinder. 

It  is  easy  to  see  that  these  projections  have  been  obtained  in  the 
same  manner  as  those  already  given  in  figs.  4  and  7  ;  that  is  to  say, 
the  external  projection,  fig.  10,  is  derived  from  the  two  right  pro- 
jections, figs.  8  and  9 — one  made  upon  an  auxiliary  vertical  plane, 
parallel  to  the  axis  of  the  piston-rod,  and  perpendicular  to  the  axial 
lines  of  the  trunnions,  and  the  other  upon  a  horizontal  plane, 
parallel  to  the  cylinder  ends,  and,  consequently,  perpendicular  to  its 
axis.  All  the  different  parts  of  this  cylinder  are,  in  fig.  10,  project- 
ed by  straight  lines  and  ellipses,  accordingly  as  they  are  rectilinear 
r. r  circular  in  contour.  It  is  the  same  with  the  section,  fig.  13, 
ind  tin-  horizontal  projection,  fig.  14,  which  are  derived  from  the 
two  right  projections,  figs.  11  and  12,  made  upon  auxiliary  planes; 
one  vertical,  and  passing  through  the  axis  of  the  cylinder,  and 
through  the  valve-casing,  whilst  the  other  is  perpendicular  to  this 
axis,  and  passes  through  the  line,  1 — 2,  fig.  11.  The  dotted  work- 
ing lines,  indicated  upon  tire  various  figures,  show  sufficiently 
clearly  the  various  constructions  necessary  to  obtain  these  oblique 
projections.  We  have,  moreover,  applied  numbers  to  the  different 
parts  projected,  and  more  particularly  to  the  axes  or  centre  lines, 
which  show  at  sight  what  parts  correspond  with  each  other  upon 
the  different  projections. 

423.  These  drawings  represent  the  cylinder  of  a  steam-engine, 


different  from  that  which  we  have  already  described.  The  pre- 
sent one  is  called  an  oscillating  steam-engine,  because,  instead  of 
the  cylinder  being  vertical  and  immovable,  it  oscillates  during  the 
motion  of  its  piston,  b,  upon  the  two  trunnions,  E,  carried  in  suita- 
ble bearings  in  the  engine-framing.  This  arrangement  of  oscillat- 
ing cylinder  has  the  advantage  of  dispensing  with  the  parallel 
motion,  and  of  attaching  the  rod,  A,  of  the  piston,  directly  to 
the  crank-pin,  to  which  its  motion  is  transmitted,  without  the 
intervention  of  any  connecting-rod.  In  the  head,  H,  of  the  rod, 
there  is,  consequently,  formed  a  bearing,  which  embraces  the 
crank-pin. 

The  bottom  of  the  cylinder  is  east  in  the  same  piece  with  it,  but 
it  has  a  small  central  opening,  for  the  passage  of  the  spindle  of  the 
boring  tool,  by  means  of  which  the  interior  of  the  cylinder  is  turned 
smooth  and  true.  This  opening  is  closed  by  a  cast-iron  cap,  f, 
bolted  to  the  bottom  of  the  cylinder.  Against  a  planed  face,  upon 
one  side  of  the  cylinder,  is  fitted  the  valve-casing,  G,  which  receives 
the  steam  direct  from  the  boiler,  and  has  within  it  the  valve,  H, 
which  has  an  alternate  rectilinear  movement,  at  the"  same  time 
oscillating  along  with  the  cylinder.  During  this  movement,  the 
valve  alternately  uncovers  the  ports,  a,  b,  fig.  11,  which  conduct 
the  steam  to  the  top  and  bottom  of  the  cylinder.  A  blade 
spring,  l,  attached  to  the  inside  of  the  valve-casing,  at  the  back  of 
the  valve,  constantly  keeps  the  latter  well  up  against  the  planed 
valve  face. 

The  steam  coming  from  the  boiler  introduces  itself  into  the  cas- 
ing through  the  passage,  c,  fig.  12,  which  communicates  with  one 
of  the  trunnions,  E,  and  the  escape  of  the  steam,  when  it  has  acted 
upon  the  piston,  is  effected  through  the  exit  channel,  d,  which  com- 
municates with  the  other  trunnion. 

The  piston,  B,  is  composed  of  a  cast-iron  body,  on  the  outer  sur- 
face of  which  is  cut  out  a  groove,  to  receive  the  hempen  packing, 
i,  partly  covered  by  an  elastic  metal  ring,  h,  coinciding  exactly  with 
the  inside  of  the  cylinder. 

Oscillating  cylinder-engines  have  always  been  admired  for  their 
simplicity  and  beautiful  action ;  but  it  is  only  of  late  years,  and 
now  that  such  superior  workmanship  is  attainable,  that  siu-h  en- 
gines have  been  constructed  of  considerable  size.  The  aptness  of 
this  arrangement  for  engines  of  the  largest  size  has  lately  been 
demonstrated  by  Penn,  in  the  case  of  the  Great  Britain,  and  other 
large  vessels. 


CHAPTER   XII. 
PARALLEL    PERSPECTIVE 


PRINCIPLES   AND   APPLICATIONS. 

PLATE   XLIL 


424.  We  give  the  name  of  parallel  perspective  to  the  represen- 
tation of  objects  by  oblique  projections,  which  differ  from  the 
preceding,  in  so  far  that  the  visual  rays,  which  we  have  hitherto 
•supposed  to  be  always  perpendicular  to  the  geometrical  planes, 
form,  on  the  contrary,  a  certain  angle  with  these  planes,  remain- 


ing, however,  constantly  parallel  to  each  other ;  from  which  it . 
follows,  that  all  the  straight  lines,  which  are  parallel  in  the  object, 
maintain  their  parallelism  in  the  picture,  according  to  this  system 
of  perspective.  Although,  in  general,  it  is  immaterial  what  the 
angle   of  inclination  is,  it  is  nevertheless   preferable,  in   regular 


\i>; 


stowaaf.  to  adopt  aoase  particular  angle  aa  •  nutter  of  o. 
which  will  U<r  Ik*  advantage  of  kiun;  Iha  mure  dui*i  - 
i  «iaglr  projection  ur  I 
i  ■  and  a'  ■',  figi    1  and  J,  be  the  two  projections  of  a 
we  wish  to  m...  myn  all  parallel ; 

rma  an  angle, 
cat.  with  the  ground  line.  : 

that  the 
instance  of  U  ■ 
horuontal  plane,  is  equal  to  ' 

..  the  point,  a,  being  that  at  which  it  Ion  fa 


.ins  of  the  various  figures  in 
it,  in  taking  the  above  straight  lii.<  - 

-    Bcient  to 
h.sUjad  of  making  the 

b  the  actual  pr  which  we  bare 

these  aame    lines   round  at  an  an^'le    of  80 ;.      Than,  I 
i  a",  k'  1',  fig.  3,  are  the  strai. 

1  lo  the  angle  in  question;  whilst,  on  the 

linea  properly  parallel  I  .tinn,  a'  b  ,  in 

on  in  parallel, 
or,  as,  .•  \\\ed,  false  p.  prism,' B,  with  a 

■ 

I  I   in  the 

a  be  stand  g  h  ij.     T 

cular  to 

■  qua!  to 

I 

ealty  projected,  to  a  b,  fig.   I.      Consequently,  if  thr... 

linea,  parallel  Ion,  the;  ■•  |  ;l|[  the 

.  :ls  we 

have  a! 
equal  lo 

'.  h  a*  and  h  f, 
»  *"•  »"'•  10  hall'  lli.-   lengths,  u'  m  and 

aa  all  tbl 

hilst  all  linea 
parallel  to  the  base  lir  . 


edges,  «./.'■• 

-.  a'  </*,  4"  t*,  V 
para.  :ie. 

It  will   be  eaiily  seen,  tliat  bj  adapting  the  anj.'lc  He  have  indi- 
■   ■  ■      • 

ray,  thai  the  0  in  parallel  |*  n 

sown  all  the  dimensions  of  ' 
■..•  hand,  we  I  widths  and  1 

ieh  are  para, 

■  r   from  an  on: 
in  which  the    n  be  |»  r- 

pandirnlar  to  tl  other  hud,  the  oblique  linsa 

■ually  pi  r|«  ndicular   to  ih. 
plane,  and  which  are  exactly  equal  to  lialf  the  actual  lengths  of 
the  latter. 

I  square, 
-.  M  I  and  9  '..  -,  h>  f  or  I  k.    < 

quentlr,  in  order  to  construct  the  perspective  or  oblique  pr 
fig.  1.  the  pfan 

the  purpose  equally  well  to  have  made  tile  '.. 

to  the  half  of  a  J  or  h  i. 

The  shaded  view,  fig.  j3.  r. ; 

pyramid,  a,  the  horixontal  pro- 

of Which   is  indicated  ill  full,  sharp  linea,  in  fig.  5,  and  the 

vertical  projection  in  dotted  linea,  in 

ling  to  the  principle  thus  hud  down,  the  pi 

ad,  in  the  tir>t  place,  by  drawing  all  the  linea  which  are 

perpendicular  and  parallel  lo  the  bai 

through  the  oj  | 

the  upper  and  lower  bases  of  the  pyramidal  frustum,  and 

plinth.     I 

to  the  I  bdeh  are 

likewise  paralli  1 to  the  former,  remain  horuontal  in  tin-  \«  ■ 
1  the  other  hand,  all  the  straight  lines,  f 

1/  r',  (' 

pendicular  to  thi 

or,  in  other  v. 

I 
of  the  two  bases  of  the  pyramidal  frustum,  a 
straight  line  in  I  then  mark  off  Iron. 

.  ..I  on  each  side  of  them,  the  1  p*,  ***, 

i 
straight 

joining  the  extreme  p 

the  linea  repreeenting  the  contours  of  the  tw  further, 

by  joiuix 

ami  eompli  te  the  w> iw, 

i.'T.    i  ition  of  a  •', 

ular  to  the  ^' 
in  the  finished  1  tamp  "it  the 

f  the  borixontal  projection  ;  thai  is,  when  the  fa 

1.  r  is  known,  a»  w.  II  other  prt  whkh  may 

Licular  to  the 
Ixi  ti  l>  c  d|  leal  projection  of  thl 


BOOK  OF   INDUSTRIAL  DESIGN. 


the  perspective  of  its  base,  abed,  will  bo  parallel  to  a  b.  Tbo 
circles  which  have  their  centres  at  o,  being  parallel  to  the  vertical 
plane,  are  represented  in  perspective  by  two  circles  equal  to  them- 
selves ;  and  their  position  is  obtained  by  drawing  through  the 
point,  o,  the  straight  line,  o'  o\  parallel  to  A  b,  fig.  1,  and  marking 
off  a  distance,  lying  equally  on  both  sides  of  the  point,  o,  equal  to 
half  the  length  of  the  cylinder,  measured  in  the  direction  of  the 
axis,  perpendicular  to  the  vertical  plane.  Then  with  the  points, 
o',  </\  as  centres,  describe  the  circles  with  the  equal  radii,  o' f  and 
u  /',  straight  lines,/1/5  and  i1  p,  drawn  tangential  to  the  circles, 
and  parallel  to  the  axis,  o1  oJ,  express  in  perspective  the  genera- 
trices of  the  two  cylinders  forming  the  contour  of  the  object. 
The  cylindrical  pieces  which  join  the  cylinder  to  the  base  are 
determined  in  the  same  manner  by  means  of  the  line,  n  na,  drawn 
through  the  centre,  n,  of  the  circle,  d  g,  parallel  to  ol  o\  and  by 
the  distances,  n  n\  n  n',  together  equal  to  half  the  actual  length  of 
these  cylindrical  surfaces.  The  base  is  drawn  as  in  the  preceding 
example. 

428.  The  example,  fig.  ®,  represents  a  cone  resting  upon  a 
cylindrical  base,  both  cone  and  base  having  the  same  axis  perpen- 
dicular to  the  horizontal  plane.  This  cone  and  cylinder  are  pro- 
jected on  the  plan,  fig.  8,  in  sharp  lines,  and  in  the  elevation,  fig.  9, 
in  dotted  lines. 

The  circles,  fig.  8,  representing  the  bases  of  the  cone  and  cylin- 
der, are  to  be  divided  into  a  certain  number  of  equal  parts ;  and 
through  the  points  of  division,  1,  2,  3,  &c,  perpendiculars  are  drawn 
to  the  ground  line,  and  are  prolonged  as  far  as  the  horizontal  line, 
a'  o',  which  is  the  vertical  projection  of  the  two  bases.  Through 
the  points,  a',  b',  c',  o',  are  drawn  straight  lines  parallel  to  A  B,  fig. 
1  ;  and  on  each  of  these  are  set  off  the  distances,  d  2',  b'  3',  c'  4', 
o'  5',  &c,  respectively  equal  to  half  the  lengths  of  the  perpendicu- 
lars, 2  a,  3  6,  4  c,  5  o.  &c,  which  operation  gives  the  points,  2',  3', 
4',  5',  &c,  through  which  an  ellipse  must  be  traced,  to  represent 
the  perspective  of  the  base  of  the  cylinder.  In  the  same  manner 
we  obtain  the  points  through  which  passes  the  ellipse,  representing 
the  perspective  of  the  base  of  the  cone. 

The  heights  of  the  cone  and  its  base  remain  precisely  what  they 
really  are,  in  consequence  of  their  common  axis  being  parallel  to 
the  vertical  piano.;  but  this  is  not  the  case  with  their  bases,  which, 
being  horizontal,  are  projected  obliquely,  in  the  form  of  the  ellipses 
we  have  just  drawn.  The  apex  of  the  cone,  at  the  upper  extre- 
mity of  the  vertical  axis,  does  not  change,  and  for  the  generatrices, 
or  sides  of  the  cone,  it  is  simply  necessary  to  draw  through  the 
apex  the  straight  lines,  o"  m  and  (?  n,  tangents  to  the  ellipse  repre- 
senting the  base  of  the  cone,  whilst  the  generatrices  of  the  cylinder 
are  tangents  to  the  two  ellipses  representing  its  upper  and  lower 
bases. 

429.  The  example,  fig.  H,  is  the  parallel-perspective  representa- 
tion of  a  metal  sphere  or  knob,  attached  to  a  polygonal  base  by  n 
circular  gorge,  forming  altogether  an  ornamental  head  for  a  screw. 
Figs.  10  and  11  are  the  horizontal  and  vertical  projections  of  this 
piece. 

We  must,  in  the  first  place,  remark  that  the  sphere,  the  radius 
of  which  is  o  a,  may  be  determined  in  its  perspective  representa- 
tion in  several  ways.  First,  by  imagining  the  horizontal  sections, 
«  b,c  d,  ef,  which  give  in  plan  the  circles,  with  the  radii,  a'  o, 


c'  o\  and  e'  o',  and  the  perspectives  of  each  of  these  circles  may 
be  obtained  by  operations  similar  to  the  preceding,  which  will  give 
a  series  of  ellipses,  to  be  circumscribed  by  another  ellipse,  tangen- 
tial to  them  all.  Second,  by  drawing  the  planes,  g  h,  ij,  parallel 
to  the  vertical  plane,  and  which  are  projected  in  perspective  as 
circles,  with  the  radii,  I"  g,  i  m,  the  centres  being  upon  the  oblique 
line,  n  n',  parallel  to  the  line,  A  B,  fig.  1,  and  passing  through  the 
centre,  o,  of  the  sphere.  The  external  curve,  drawn  tangential  to 
all  these  circles,  will  be  elliptical,  as  in  the  preceding  method,  and 
represent  the  perspective  of  the  sphere.  Thirdly,  by  at  first 
drawing  through  the  centre,  o,  an  oblique  line,  n  ri ;  then  a  per- 
pendicular, e  e",  passing  through  the  same  point.  Then  set  out 
from  the  centre,  o,  and  on  each  side,  the  distances,  o  e,  o  e",  equal 
to  the  radius,  o  a,  of  the  sphere,  which  gives  the  conjugate  axis  of 
the  ellipse.  To  obtain  the  transverse  axis,  it  will  be  necessary  to 
draw  tangents  t»  the  great  circle  of  the  sphere,  parallel  to  the 
oblique  ray  of  projection,  A  e,  fig.  1,  as  brought  into  the  vertical 
plane.  This  line  is  brought  into  the  vertical  plane,  as  at  a"  b.  in 
the  following  manner : — At  the,  point,  a,  a  perpendicular  to  A  B  is 
erected,  and  the  distance,  a*  a,  is  made  equal  to  a  a',  when  a"  b  is 
joined. 

These  tangents  touch  the  sphere  in  the  points,/  /',  which  may 
be  obtained  directly  by  drawing  through  tho  centre,  o,  the  line,//, 
perpendicular  to  a"  b.  These  tangents,  further,  meet  the  line,  n  n', 
in  the  points,  n,  n' ;  and  the  distance  between  these  points  is,  con- 
sequently, the  transverse  axis  of  the  ellipse,  which  represents  tho 
perspective  of  the  sphere,  and  which  may  be  drawn  according  to 
any  of  the  known  methods. 

This  last  method  is  evidently  the  shortest  and  simplest  of  the 
three  for  obtaining  the  perspective  of  the  sphere,  but  it  is  confined 
in  its  application  ;  for  any  other  surface  of  revolution,  as,  for  exam- 
ple, the  gorge,  which  unites  the  sphere  to  the  hexagonal  base, 
cannot  be  defined  in  this  way.  In  cases  where  the  axis  of  the 
surface  of  revolution  is  vertical,  as  in  this  example,  it  will  be  neces- 
sary to  adopt  the  first  general  method,  which  consists  in  taking 
horizontal  sections..  When,  on  the  other  hand,  the  axis  of  the 
surface  of  revolution  is  horizontal,  we  must  employ  the  second 
process,  which  consists  in  taking  sections  parallel  to  the  vertical 
plane,  or  perpendicular  to  the  axis.  Tho  perspective  of  the  thread 
of  the  screw,  of  which  the  sphere  is  the  ornamental  head,  is  de- 
terminable in  a  manner  analogous  to  that  of  a  circle.  It  is  suffi- 
cient, in  fact,  first  to  draw  the  two  geometrical  projections,  figs.  8 
and  12,  of  one  or  two  convolutions  of  the  thread,  and  to  find  the 
perspectives  of  the  very  points  which  have  served  for  the  construc- 
tion of  the  helices.  Thus,  for  example,  we  put  the  circle,  I  p  q, 
fig.  8,  into  perspective,  as  at  P  p'  q',  fig.  13,  retaining  for  this  pur- 
pose the  same  points,  I,  p,  q,  &c,  which  were  employed  in  deline- 
ating the  screw,  fig.  12.  Through  these  points,  P,p*,  q1,  &c,  draw 
vertical  lines  ;  and  upon  them  set  off'  the  distances,  V  P,  P  P,  pl  p', 
&c.  Then  through  the  points,  P,  P,  &c,  draw  the  curve,  which 
will  be  the  perspective  of  the  outer  helix  of  the  screw-thread. 
By  going  through  the  same  operation  for  the  inner  circle,  r  s  t,  ficr. 
10,  we  shall  obtain  the  similarly  perspective  outline  of  tho  inner 
helix. 

An  examination  of  fig.  13  will  further  show  that  the  heights  on 
the  vertical  lines  are  precisely  the  same  for  both  helices,  for  they 


■'I  \\s 


an  uln  upoa  raJB  tommcm  to  the  two  circlea,  /*»*  and  M 
• 

,»•  J.-  med  it  nimrrrwrr  to  •titer  further  into  the  devc- 
I711I  of  this  apscwa  of  perspective,  of  which  we  hare  already 
p.ra  a  erorrml  appfieatiun  in  the  boring-machinc,  n-pn- 

.1  rxatuple  in  which  are  collected  almost  all 
• 
Mechanical  elements  and  MMI 

In  that  example,  a>  figBXM  in  Plate  \1.II ,  which 

or  lisual  rara  to  be  in  all  cases  para.  XT,  uu>l  to  be 


inclined  at  an  ai  al  pro- 

.reee  all 
that  tw  11  do,  allowing 

: 
may  !*•  ujs.n  1. 

nd  the  utility 
ing,  at  a 

• 
metrical  ID  greatly  simplify  the 

proeeaa  of  sketching  l.i.  uncry. 


CHAPTEB   XIII. 

T  1:  r  1:   p  1;  i:.-1'i:cti  v  E. 

■■:■    APTLICATIOXS. — ELEMEXTAKY    RDORla 

l'l.ATE  XLI1L 


430.  Perspe.  -.ralhsl — bat  here  defined  M  1 

a  (undid  nr  [alee  perspective,  in  its 
upon  the  actual  manner  in  which  v  i-i^n  tak.  - 
that  is,  tliat  instead  of  being  parallel  to  Men  other,  tin-  visual  rays 
jcet  is  said  to  bo  drawn  in  pen 
tng  tlie  drawing  fron  a  |urticul.ir  point,  it  | 
the  aame  appearance  t..  the  organ*  of  »i=ion  as  the  object  refjro- 
;  we  when  aimila 

travel    from    the    object    in 
tig  to  a  point  at  the  eye,  and  forming  a  cone 
of  ray*  to  be  intercepted  bj  a  tnms- 

parent  plane,  or  diaphragm,  of  any  form — tin  11.  Di 

«  from  the  rations  |urt-  of  the  object   pierce  this 

diaphragm,  let  us   paint    up-.n  it    t!  I  te  me 

-hull   have  the  ev;u-t  appear- 

taelf,  modified,  as  they  may  l»-,  by 
.  ami  by  their  U iiig  in  the  light  0 

in  n|"'ii 

the  diaphragm  will   11  I  00   upon   lie 

I 
>l  and  natural  manner,  that   the  art  of  draw 
• 

TTie  fixed  point,  to  which  the  ray-  lOed  the  point 

.  and  in  diagrams  explanatory  of  j 
together  with  • 

the  picture.       I  n  of  an 

lathematically,  we  must  have  given  us  the  horizontal  and 

and  the    position  of   the  plat 

■ 
rays  as  paaaing  from  the  »arious  jw.ints  of 

.  of  those  rays  with  I 
of  the  picture. 


FIRST  PROBLEM. 

THE    rEBsrECTIVE    OF    A    HOLLOW   miSM. 

431.  I>et  A  and  a',  figs.  1  and  2,  bo  the  horizontal  an  i 
DS  of  the  prism  which  we  wish  to  il,  line  ale  in  p-  r- 

the  point  of  sight  being  projeeled  in  v  and  v',  and  the  pla: 
picture,  in  T  and  t\  p  I   to  Ik-  |wpfiidicul.ir  to   tlio 

planes  of  projection,  snd  \ert:  ally  the  case. 

Through  the  point,  t,  in  the  borl 
rays  from  each  of  the  | 

contour  of  the  prfaau.    The  Intersection  oi  sriththe 

plane  of  the  picture  determines  the  points,  I*,  a1,  e",  a",  srhi 

upon  the  hori  11,  T  0,  of  the  latter,  the  pi  I 

of  the  point*,  ". 

In  like  manner,  through  the  point,  v'.  in  the  vertical   projection, 
draw  the  vianj 

the  picture  in  the  points,  «*,»',/*, and  **;  : 

qoently,  the  vertical    projections  of  I 

to  the  plane  of  the  picture, 
the  perspective  of  the  object  is  do!  \ i-il.l.-.  sines  all  the  points  are 
1  in  the  vertical  line,  T  T  ,  tie 

■  plane  as  turned  over  upon  tie 

.- ;  whilst  we  mnat  mppoM  the  line,  t  0,  the 

horizontal    projection  of   the  picture-plane,  as  turned    about    the 
..-  a  e.ntrc,  through  a  right  angle,  bringing  it  to  coincide 
with  the  ground  line,  L  BL      Winn   this  is  done,  the   potntl 
r',  aP,  will  ill— libit  ar  -  -.1.  finally,  coincide  with  the 

1  B   the  ground  line.     Next,  upon  ti  • 

the  horizontals,  drawn  through   the 

• 

will  be  the  parspectjvsa,  a',  b',  c',  d\  of  the  comers,  o,  6,  c,  d,  ot 


BOOK   OF   INDUSTRIAL   DESIGN. 


the  top  of  the  prism.  We  have,  likewise,  the  points,  e'',f',g,  h,  for 
the  perspectives  of  the  corners  of  the  bottom  of  the  prism,  which 
is  parallel  to  the  top;  consequently,  by  joining  all  these  points 
together  in  couples,  as  indicated  in  fig.  A,  we  obtain  the  entire 
perspective  of  the  externa!  outline  of  the  prism.  As  the  prism  is 
hollow,  we  shall  see  in  the  perspective  view  the  outline,  i'  m!  n'  o', 
corresponding  to  the  edges  of  the  part  hollowed  out. 

The  point  of  sight,  of  which  v  and  v'  are  the  geometrical  projec- 
tions, is  projected  upon  the  picture-plane  in  the  points,  v,  v";  and 
when  the  picture-plane  is  turned  over,  the  point  will  be  found  at  i>", 
which  is  the  position  of  the  point  of  sight  upon  the  perspective 
drawing. 

It  must  be  observed,  that  in  this  example  the  lines,  a*  b',  a'  d*, 
and  i*  c',  which  express  the  perspective  of  the  corresponding  lines, 
a  b,a  d,  and  b  c,  are  the  intersections  with  the  plane  of  the  picture, 
of  planes  passing  through  these  lines,  and  through  the  point  of  sight. 
Now,  since  the  intersection  of  two  planes  is  always  a  straight  line, 
the  following  conclusions  may  be  drawn  ;  that, 

432.  First,  The  perspective  of  a  straight  line  upon  a  plane  is  a 
straight  line. 

It  may  also  be  remarked,  that  the  verticals,  such  as  i*  e',cth,dt  g, 
are  the  perspectives  of  the  vertical  edges,  projected  in  the  points, 
b,  c,d;  whence  we  deduce  that, 

433.  Secondly,  The  perspectives  of  vertical  lines  are  verticals, 
when  the  plane  of  the  picture  is  itself  vertical. 

It  will  further  be  seen,  that  the  horizontals,  I*  c*,  d*  a',  e'  h,f  g, 
of  the  perspective  view,  correspond  to  the  straight  lines  projected 
horizontally  in  b  c  and  d  c,  which  are  parallel  to  the  picture; 
whence  it  may  be  gathered,  that, 

434.  Thirdly,  The  perspective  of  any  straight  horizontal  line, 
parallel  to  the  picture,  is  itself  horizontal. 

Further,  it  follows  from  the  two  preceding  principles,  that  all 
lines  parallel  to  the  plane  of  the  picture  are  represented,  in  per- 
spective, by  lines  parallel  to  themselves. 

Finally,  the  straight  lines,  a'  b',  d*  c',  e*  f,  and  h  g,  which  all 
converge  to  the  same  point,  v",  the  projection  of  the  point  of  sight 
upon  the  plane  of  the  picture,  correspond  to  the  edges,  ab,  dc,ef 
v.  hich  are  horizontal,  but  perpendicular  to  the  plane  of  the  picture ; 
whence  it  follows,  that, 

435.  Fourthly,  Tlie  perspectives  of  lines  which  are  horizontal,  but 
perpendicular  to  the  plane  of  the  picture,  are  straight  lines,  which 
converge  to  the  point  of  sight,  and  are  consequently  foreshortened. 

It  will  be  seen,  from  figs.  1  and  2,  that  the  whole  width  of  the 
perspective  representation,  fig.  A,  is  comprised  between  the  points, 
i"  and  <fa,  which  He  on  the  outermost  visual  rays,  drawn  in  the 
horizontal  projection ;  and  that  its  height  is  limited  by  the  two 
points,  a"  and  e",  which  correspond  to  the  extreme  visual  rays  in 
the  vertical  projection.  The  angle  formed  by  the  extreme  visual 
rays  is  termed  the  optical  angle.  In  the  present  example,  this  angle, 
V  v  d',  in  the  horizontal  projection,  differs  from  the  angle,  a"  v'  e", 
in  the  vertical  projection. 

The  positions  of  the  object  and  point  of  sight  being  given,  the 
dimensions  of  the  perspective  representation  vary  according  to 
the  position  of  the  plane  of  the  picture.  It  will  thus  be  seen,  on 
referring  to  fig.  I,  that  if  this  plane  be  removed  from  if  to/  t', 
nearer  to  tlie  object,  the  limits  to  the  perspective  representation 


by  the  extreme  visual  rays  will  be  enlarged  ;  whilst,  on  the  con- 
traiy,  if  we  remove  the  plane  of  the  picture  to  the  position,  /"  C, 
nearer  to  the  point  of  sight,  the  limits  will  be  sensibly  narrowed. 

Again,  if,  in  place  of  moving  the  plane  of  the  picture,  the  point 
of  sight  is  removed  further  off,  or  brought  nearer  to,  the  size  of  the 
perspective  outline  will  thereby  be  augmented  or  diminished.  It 
may  therefore  be  concluded,  that, 

430.  Fifthly,  The  dimensions  in  the  perspective  representation  do 
not  wholly  depend,  cither  on  the  actual  size  of  the  object,  or  on  the 
distance  from  which  it  is  observed,  but  also  on  the  relative  distances 
of  the  point  of  sight  and  of  the  object  from  the  plane  of  the  picture. 

Thus  the  sides,  d  a  and  c  b,  fig.  1,  are  actually  equal,  but  the 
former  is  further  from  the  plane  of  the  picture  than  the  latter;  so 
that  whilst  this  is  represented  by  the  space,  c'  b',  fig.  A,  that  is 
limited  to  the  much  smaller  space,  d*  a',  in  the  perspective  view. 


SECOND  PROBLEM. 

THE    PERSPECTIVE    OF   A   CYLINDER. 
FlGDRES    3    AND    4. 

437.  To  obtain  the  perspective  outline  of  a  vertical  cylinder,  such 
as  the  one  projected  horizontally  in  B,  fig.  4,  and  vertically  in  b', 
fig.  3,  we  proceed,  as  in  the  preceding  example,  to  draw  through 
the  point  of  sight,  v'  v,  a  series  of  visual  rays,  extending  to  the 
various  points,  a,  b,  c,  d,  e,  taken  on  the  upper  end  of  the  cylinder, 
by  preference  at  equal  distances  apart.  These  lines  intersect  the 
plane,  T  t',  of  the  picture,  in  the  points,  d\  c',  a',  g*,  &c.,  in  the 
horizontal  projection,  and  in  the  points,  a",  c",  d",  Sua.,  in  the  verti- 
cal projection. 

By  bringing  the  plane,  T  t',  of  the  picture,  into  that  of  the 
diagram  before  us,  or  what  is  equivalent  to  it,  by  finding  the  points, 
g',  a3,  Sic,  by  means  of  arcs,  drawn  with  the  centre,  o,  on  which 
the  plane  is  supposed  to  turn,  and  drawing  the  horizontal  lines 
through  the  corresponding  points  in  the  vertical  projection  of  the 
picture-plane,  we  obtain  the  points,  c4,  d*,  a',  g*,  &c,  which  are 
points  in  an  elliptic  curve  representing  the  top  of  the  cylinder  in 
perspective,  which  is  visible,  in  consequence  of  the  point  of  si^ht 
being  above  it. 

The  same  points,  a,  b,  c,  d,  of  the  horizontal  projection,  give,  in 
combination  with  their  vertical  projections,  g1,  f",  c",  &c,  the  per- 
spectives, dB,  eb,fb,  gb,  of  the  bottom  of  the  cylinder,  of  which, 
obviously,  only  a  part  is  visible. 

The  two  vertical  generatrices,  d*  d6,g-'g5,  being  drawn  tangential 
to  the  upper  and  lower  ellipses,  complete  the  perspective  outline 
of  the  cylinder,  fig.  13. 

As  this  cylinder  is  hollow,  an  operation  similar  to  the  preceding 
will  be  called  for  in  delineating  the  upper  visible  edge  of  the  hoi- 
Ipwed-out  portion. 

It  must  be  observed  that,  in  taking  an  even  number  of  divisions, 
at  equal  distances  apart,  upon  the  horizontal  projection  of  the 
cylinder,  and  setting  them  off  from  tlie  diameter,  c  g,  parallel  to 
the  plane  of  the  picture,  we  have  always  a  couple  of  points  situated 
upon  the  same  perpendicular  to  the  plane,  and  of  which  the  per- 
spectives are,  consequently,  situated  on  the  same  straight  line, 
drawn  through  the  projection,  v",  of  the  point  of  sight.      This 


160 


TIIK    PRACTICAL   DRAUGI11 


upoa  the  liar,  i'  J".  »••  that 

I...    j :..    ■!.:.„•  MMini  tioO- 


Ti:  M. 

THE    rr 

asv  Rinn 

BBS  i  A.1D  A. 

bt,  ritu- 
2  through  thi 
the  nolid,  r  c',  srnl  j- -  •  picture. 

J  line,  i '  i",  repreaenting  the 
which  all  Uic  I 

and  c  </,  which 
of  tin-  picture,  and  which  an 

i'  b*  ami  if  e*i  laith  directed  to 
ma  with  the  tdgm,fg,  h  i,  of 
•    v  V  i',  likewise  oonvei 

they  retain  their  rertical  position  in 

.  ami  the  horizontal  lines,  a  il.  I  rn.  n  k.  e  0,  parallel 

ire,  are  rendered  in  the  perspective  view  by 

parallels,  such  as  a*  if,  f  at*,  n'  K',  r'  i'. 

It  nat]  on  of  this  problem,  that  when- 

■  through  the  aids  of  ■ 

:i  1  perpendicular  to  the  plat  ore,  the 

imetrical  with  n 

that  it  is,  th<  rt  fore,  qnita  sufficient  to  go  throngb 

,  ■  only  of  tin   I 


POl  RTH  PROBLEM. 

E   OF   A    HEARING-BRASS,    PLAi  r.H    WITH    ITS    AXIS 
.  II  A  I.. 

I1..1  m  7  1 

situated,  as  in  the  pn 

h  the  a\i-  of  tl bjoct, 

the  picture-plane,  the  perspective  will  like- 

trical  in  reference  to  the  centre  line,  i'  r*j  and  it  is 

■  uliaritv  further.     The  Inside  of  Ihe 

••  rmlnated  by  horizontal  semi- 

I  will  !"•  r.  nd 
I  which  it  will  Ik>  sufficient  to 

'     '  to  tli" 

ghl  line,  a  e,  which  is  horizontal  an. I  parallel 

••  avis,  /,*  ,/•,  is  eqaa]  to 
i  ..r  /.'  </',  which  is  alsn  horizontal, 

.'.      It  will  !«•  remarked,  that  the 


H  the  jxiint  of 

III  II I  PROB1 

Till:    I  A    SFH1EICAL    BOSS. 

-    '.I    AM'     HX 

tin.  in  carrying  oat  the  general  principle,  it  will  be  coi 
that,  in  1 
should  draw  tin 

1  ut  in  order  to  ascertain  the  i 
tact  of  tl 

■  g  through  the  sphere,  producing  circular  - 
ami  then  to  find  the  perspective  of  each  of  these  circles, 
being  found,  ■  curve,  drawn  to  oircomscribe  them,  will  be  the 

the  sphere. 

In  the  example,  lii--.  9  and  10,  the  pofa 
chosen  aa  befon — that  is.  as  situated  in  ..  | 
the  centra  of  the  Bphere,  add  perpendicular  to  the  picture-] 
the  perspective  of  the  sphere  will,  on  this  account,  simply  be  an 
ellipse,  having  for  conjugate  axis  the  base,  o*  /•',  of  the 
•  v  A.  in  the  horizontal  projection  ;  and  tor  transvi  ■ 
the  base,  r'  if,  of  the  angle,  e*  V  <P,  in  the  vertical  projection; 
because  the  right  cone,  formed  by  the  series  of  visual  i 
gential  to,  and  enveloping  the  sphere,  ia  obliquely  inter-. 

the    plane   of  the    picture.      If.  however,   the  point   of  sight   Were 

situated  upon  a  horizontal  line,  passing  thr  . .  o,  of 

the    sphere,    |h  of    the    latter   Would   I 

The  spherical  pari  of  the 

•  ption  of  the  key,  an. I  the  edge,*  /,of  this 

.  being  situated  in  a  plane  parallel  to  Ihe  pictui 
will,  in  i1  .  Bg,  B,  be  rendered  by  a  circle,  of  which  the 

i  the  cylindrical  Iher  side  of  the  stopcock,  for 

iu  junction  with  a  lii  alclrcle,  ag  h.  is 

ted  by  a  portion  of  an  ellipse,  having  the  horizontal  line, 
a'  h'.  corresponding  to  .<  /<:  and  the  vertical,  g*c*,  being  the  per- 
spective at g*  '•'■  The  circle,  <<  h  bg,  the  horizontal  projection  of 
tin.  surfa. I"  (In-  npp  i-  n  presented  in  ihe  perspec- 

tive view  by  I  |  S«  is  also  the  upper  visible  ■ 

the  inner  tubular  p  irtion.     Bui  this  is  the  same  as  tin-  eaai 
the  ellipses  may  be  formed  in  a  similar  manner. 
The  perspective  representation  of  a  circle,  however  situated, 

otherwise  than    parallel  with   regard  to  the  plane  of  the  picture,  i- 

alwaya  a  perfect  ellipse ;  but  the  transverse  avis  ol  I 

th,  or  is  not   the  representation  of,  any  dial 

the  circle  ;  for  it  is  evident,  that  the  more  distant  half  of  the  circle 
must  be  d  must  occupy 

pace   than   the  anterior  half,  whilst  the  ellipse   is 

iliviilnl  b 


BOOK   OF   INDUSTRIAL  DESIGN. 


V\  hen  the  point  of  sight  is  in  a  line  perpendicular  to  the  circle, 
the  rays  from  the  latter  will  form  a  right  cone  ;  and  if  the  plane  of 
the  picture  is  not  parallel  to  the  circle,  the  section  determined  by 
it  will  be  an  ellipse,  as  is  well  known.  Again,  if  the  circle  is  not 
perpendicular  to  the  central  visual  ray,  the  cone  of  rays  will  be 
elliptical,  and  the  sections  of  such  cone  will  be  ellipses,  of  various 
proportions,  that  parallel  to  the  circle,  however,  being  a  circle. 

The  transverse  axis  of  the  perspective  ellipse  is  the  perspective 
of  that  chord  in  the  original  circle,  which  is  subtended  by  the  arc, 
between  the  points  of  contact  of  the  extreme  visual  rays,  as  pro- 
jected ill  the  plane  of  the  circle. 


SIXTH  PROBLEM. 

t\ie  perspective  of  an  object  placed  in  ant  position  with 

regard  to  the  plane  of  the  picture. 

Figures  11  and  12. 

441.  In  each  of  the  preceding  problems,  we  have  supposed  one 

or  other  of  the  surfaces  of  the  objects  to  be  parallel  or  perpendicular 

to  the  plane  of  the  picture ;  but  it  may  happen  that  all  the  sides  of 

the  object  may  form  some  angle  with  this  plane.     It  is  this  case 

which  we  propose  examining  in  figs.  11  and  12. 

Let  a  be  d  be  the  horizontal  projection  of  a  square,  of  which 
the  sides  are  inclined  to  the  plane,  t  t',  of  the  picture,  and  of 
which  it  is  proposed  to  determine  the  perspective.  The  point  of 
sight  being  projected  in  v  and  v',  if  we  employ  the  method 
adopted  in  figs.  1  and  2,  we  shall  find  the  points,  a',  b2,  c1,  d\ 
to  be  the  horizontal  projections,  and  a",  b',  c",  d",  the  vertical 
projections  of  the  corners  of  the  square;  and  when  we  have 
brought  the  plane  of  the  picture,  T  t',  into  the  plane  of  the 
present  diagram,  as  before,  we  shall  find  the  actual  positions  of 
these  points  to  be  at  a',  ft\  c',  d*.  If  we  join  these  points,  we 
shall  have  a  quadrilateral  figure,  of  which  the  two  opposite  sides, 
a*  J4,  c'  dl,  converge  to  the  same  point,  /,  whilst  the  other  two 
sides  converge  to  the  point,  /'.  These  two  points  are  termed 
vanishing  points.  They  are  determined  geometrically,  by  drawing 
through  v,  the  horizontal  projection  of  the  point  of  sicrht,  the 
itraight  lines,  v  t  and  v  t',  parallel  to  the  sides,  a  b  and  b  c,  of  the 
given  square,  and  prolonging  these  lines  until  they  cut  the  line, 
T  T',  representing  the  plane  of  the  picture.  Having  drawn  through 
v'  the  horizontal,  v'  v',  termed  the  horizontal  line  or  vanishing 
plane,  set  off  the  distance,  v  t,  from  v"  to  /  and  the  distance, 
v  T',  from  v"  to  f,  and  /  and  /'  will  be  the  required  vanishing 
points. 

It  follows  from  the  preceding,  that 

When  the  straight  lines  which  are  inclined  to  the  plane  of  the 
picture  are  parallel  to  each  other,  their  perspectives  icill  converge  in 
one  point,  situated  on  the  horizontal  line,  and  termed  the  vanishing 
point. 

When  several  faces  or  sides,  situated  in  different  planes,  are 
parallel  to  each  other,  their  perspectives  all  converge  to  the  same 
vanishing  point,  which  allows  of  a  great  simplification  of  the 
operations. 

Thus,  the  edges  of  the  horizontal  faces,  h!  i'  and  h"  i',  of  the 
quadrangular  prism,  being  respectively  parallel  to  the  sides  of  the 


square,  a  bed,  are  represented  in  perspective  by  the  straight  lines, 
tV,  i*  e',  converging  to  the  first  vanishing  point,/,  and  the  straight 
lines,  i3  g',  i*  g',  converging  to  the  second  point,  f. 

The  cone,  f  f',  which  is  traversed  laterally  by  the  prism,  has  its 
apex  projected  horizontally  in  the  point,  s,  fig.  12,  and  vertically  in 
the  point,  s',  which,  with  its  axis,  appertains  to  fig.  11.  The  per- 
spective of  the  point,  s  s',  on  the  plane  of  the  picture,  is  found,  in 
the  usual  way,  to  be  at  s  in  the  horizontal  projection,  and  at  s'  in 
the  vertical  projection  ;  and  when  the  plane  of  the  picture  is  brought 
into  the  plane  of  the  diagram,  these  points  are  represented  by  the 
points,  s2  and  s",  upon  the  same  vertical,  s3  o',  which  is,  consequently, 
the  perspective  of  the  axis,  o  s',  of  the  cone,  and  the  point,  s2,  is 
the  perspective  of  the  apex  of  the  cone. 

If  we  draw  the  perspectives  of  the  two  bases,  k  I  and  m  n,  of  the 
frustum  of  a  cone,  according  to  the  methods  already  given,  it  will 
only  remain  to  draw  through  the  point,  s3,  the  two  lines,  s"  m!  and 
s2  n,  tangential  to  the  ellipses,  representing  the  bases,  which  will 
complete  the  perspective  of  the  entire  object,  as  in  fig.  [p\ 


APPLICATIONS. 
FLOUR- MILL    DRIVEN    BY    BELTS. 

PLATES  XLIV     AND  XLV. 

442.  The  elementary  principles  of  perspective  which  we  have 
laid  down,  will  admit  of  application  to  the  most  complicated  sub- 
jects, and,  among  other  things,  to  complete  views  of  mechanical 
and  architectural  constructions.  In  Plate  XLV.  we  have  given 
an  example,  which  will  enable  the  student  to  form  a  general  idea 
of  this  branch  of  drawing.  This  Plate  is  the  perspective  repre- 
sentation of  the  machinery  of  a  flour-mill  driven  by  belts,  and  Ha 
fitted  up  by  M.  Darblay,  at  Corbeil.  Before  proceeding,  however, 
to  discuss  this  as  a  study  of  perspective,  we  propose  to  describe 
the  various  details  of  the  mechanism  composing  the  mill,  and 
which  we  have   represented,  in   geometrical   projection,  in  Plato 

xliv. 

The  construction  of  flour-mills  has  latterly  undergone  very  in. 
portant  improvements,  as  well  in  reference  to  the  principal  driving 
machinery,  as  to  the  minor  movements,  and  the  cleaning  and 
dressing  apparatus.  As  such  machinery  belongs  to  a  most  impor- 
tant class,  we  have  selected  a  mill,  as  an  illustrative  example  of  the 
subject  before  us,  giving  all  the  recently  improved  modifications 
now  at  work,  both  in  this  country  and  on  the  Continent. 

443.  Before  the  introduction  of  what  is  known  as  the  American 
system,  very  large  uncovered  millstones,  of  upwards  of  six  t'eet,  or 
two  metres,  in  diameter,  were  employed  ;  and  these  gave  what  were 
then  considered  very  good  and  economical  results.     These  mills 

.were  worked  by  water-wheels  or  wind-wheels;  but  as  improve- 
ments gradually  crept  in,  not  only  was  the  entire  internal  mechanism 
changed,  but  also  the  motor,  and  the  description  of  stones.  The 
American  flour-mills,  commonly  known  on  the  Continent  as 
English  mills,  differed  from  the  older  mills  in  the  employment  of 
smaller  stones,  with  furrowed  surfaces,  and  in  their  being  driven 
at  a  much  greater  speed,  requiring,  in  consequence,  more  wheel- 
gear  to  bring  up  the  speed.     A  mill  on  the  old  system,  with  large 


I«J 


t  'in  (batter,  ordlnari ly  goes  at  the  rate 
60  rvTolutioat  per  nvnute,  t*  in*   Bored,  we  dull  .up;- 

■  V«(,  caLr.;  10  ur   IS  turne   in  the  «an>. 
■m!l  »ul  I'C'i  ■  I  and  »  lanterr. 

or  better,  a  av. 
• 
Bat  a  modem  mil: 

'  nt  be  imp> ' 

■aJflft/talf  gear!    ^t»:»i.nth'   p.wcr  and  the  w  .irk.     When  this 
mu'tl;-'-.  .iti  n  is  obtai: 

eataaatiaf  «f  a  ana  horizontal  ajmr-wh.-, ■!.  drhin;;  a  spur-pinion 

c-   •  •;  .•->••'_»  l->:i  sup  r~  h-i.  in   many 

•  has  the 
»  !  ■  -  ■ 
the  at  ppafc  "f  »  •  r.J-  [^  :•  ■•:' -:  on,  w ithout  ^ t ■  *i -(*"*> _r  the  ;■  ■-.■  n» 

■  asaj   ■  i   :'•..■    w1    lie    !:.     .  '  !     i  i-  J  !■•;  >•«  nti.il   point,  more 
i  large  and  importa;  I  t.iany  pairs  of 

atones  an-  at  •• 

The  drawing.  Plata   XI.1V  .  mil!  of  thi* 

1  tarblay,  at  Cor 
c<npri-   ■  The 

■ 
I 

- 

aa  Car  aa  the  vertical  al 

vertical  section,  taken  at  rijjht  anj.    • 

■■ft. 

r  end  of  th« 

-  down. 

ty.  and 

in  a  lira--  "ing  in 

- 
;rnal,  6, 
of  the  main  driving-ahaft,  r. 

'.oft,  t,  lia»  fixed  upon  it.  in  U  -jHnion, 

•  heel,  c,  fitted  with  m 
• 

wrooght-iron  shaft,  a',  which  paaaca  up  to  U 

buildin.  rariooa  accessory  apparatus 

•  •f  the  mill,  auch  a*  the  aack-hoieta,  preanit  . 

■ 
•hat  shown  in  section  at  d,  in 

-   aa  at  e, 

- 
aeerrer  at  the  top,  at, 

-'.-lndards 
:>ii  brass 


-■••■_- 

necessary;  aii  ;  the  in. 

»iiirh  ia  bolted  to  the  croaa  beams  of  tha 

■ 

.!  shafts,  i.  ha- 

Tlie   piniona   gear   « 

- 
shaft,  E  ;  and  tl  it  in  commu- 

These  but  are  each  keyed  upon  tt 
atones,  ■.     A  tension  ; 

y  the  two  arms  of  a  aecor 

• 

a  eoople  of  guide-pulleys.  /,  and  ai 

• 

communicated  to  the  pulleys,  l'.     1'.  ted  up, 

tension 

I ;  and  the  !••  .  will  no 

-  communion-  .  and  consequ. ; 

pairs  of  stones,  will  1-  ilea  o,  are  sup- 

•  bearing*,  carrii-d  by  cast-  i  to  the 

■a  beams.     T  an   thus 

ball  when 

-lack,  iron  f  ..  ed  at  intervals,  attached  to 

■ 
millstone  shaft  is  generally  made  of  cast-iron,  its  lower 
end  is  fitted  w  ith  a  caj 

i  of  a  brass  f. 

cup,  r, 
formed  in  uV  rfaian  surmounts 

;»'n  which  the  entire  framr  .■ 
• 

tbe  shaft 
•  liaft  is  adjusted  vertically,  ai: 
■ 

.  has  a  small   -  a  Inch  a 

small  pa  ..ndle.  r, 

upon  its  vertical  spindle.     By  turning  this  handle  I 
.  the  small  wheels  are  set  in  motion ;  and  a- 
cannot  otherwise  turn,  it  i«  (breed  to  rise  or  fall,  and  with  it  the 

•  manner 
• 

.  iccording  to  t 

.ft  is  also  case-hardened,  and 
-ain  distance  into  the  boss  • 
-  fi-ed  acmes  the  eye  of  the  -  runner, 

•  -mly  imbedded   into    the  stone  at  either  aide.    On  the 


BOOK  OF    INDUSTRIAL  DESIGN. 


top  of  the  boss  of  the  centre-piece,  u>,  is  a  species  of  metal  saucer, 
Jito  which  dips  the  lower  end  of  the  pipe  which  conducts  the  grain 
iown  from  the  funnels,  R,  generally  made  of  copper.  These  fun- 
nels, which  receive  the  grain,  communicate  by  the  pipes,  y,  with  a 
single  hopper  above,  and  rest  upon  the  wooden  cross-pieces,  s,  fig. 
2,  held  down  on  one  side  by  a  hinge,  z,  and  on  the  other  by  a 
vertical  iron  rod,  z',  by  means  of  winch  they  are  raised  or  lowered 
at  pleasure,  so  as  to  set  the  bottom  of  their  pipes  at  a  greater  or 
less  distance  above  the  bottom  of  the  saucer  below.  The  object 
of  this  arrangement  is  to  allow  nioro  or  less  grain  to  enter  between 
the  stones.  The  supports  of  the  cross-pieces,  s,  are  fixed  upon  a 
wooden  casing,  T,  which  covers  each  pair  of  stones,  a  space  being 
left  inside  all  round  the  stones,  into  which  the  produce  of  the 
grinding  falls,  as  it  issues  from  between  the  stones.  It  is  thence 
conducted,  by  suitable  channels,  either  to  receiving-chests,  or  to  the 
elevators,  by  which  it  is  carried  to  the  upper  part  of  the  building, 
to  undergo  the  subsequent  processes. 

The  lower  immoveable  stones,  q',  of  the  same  diameter  as  the 
runners  above,  are  fitted  with  metal  eyes,  b',  furnished  with 
brasses,  which  embrace  the  shafts  of  the  runners,  and  assist  in  pre- 
serving their  perfectly  vertical  position.  These  stones  are  grooved, 
as  indicated  in  the  plan  of  one  of  them,  fig.  1  ;  thai  is  to  Bay,  shal- 
low channels  are  cut  out  of  their  working  surfaces,  so  as  to  present 
on  one  side  a  sharp  edge,  and  act  with  the  runner  like  scissors, 
cutting  each  grain  as  it  comes  upon  them.  The  fine  close-lined 
dressing,  which  is  given  to  the  surface  between  these  channels, 
completes  the  fracture  and  crashing  of  the  grain.  These  lower 
stones  rest  upon  the  cast-iron  plates,  u,  but  with  the  intervention 
of  the  three  adjusting  screws,  a',  which  allow  of  the  obtainment 
cf  an  exact  level;  whilst  four  lateral  screws,  a!,  fig.  1,  entered 
through  the  lateral  cast-iron  frame,  serve  to  adjust  wilh  accuracy 
the  centre  of  the  stone. 

The  base  plate  and  side  frames  are  not  only  bolted  to  the  cross 
beams  of  the  building,  but  they  are  also  supported  at  intervals  by 
cast-iron  columns,  v,  placed  between  each  pah  of  stones,  and 
resting  upon  the  plates,  o',  and  the  solid  masonry  below  them. 
The  ceiling  is  additionally  supported  by  the  solid  wooden  columns, 
x,  placed  at  the  ends  and  between  the  two  rows  of  stones.  An 
iron  railing,  v,  is  placed  on  each  side  of  the  driving-gear,  to  prevent 
accidents  which  might  arise  from  persons  passing  too  near  the 
heavy  wheels.  Cavities  are  constructed  in  the  masonry,  for  the 
reception  of  the  mechanism  for  adjusting  the  footstep-bearings  of 
the  runner-shafts,  already  described.  These  openings  are  usually 
covered  by  suitable  doors. 


THE  REPRESENTATION  OF  THE  MILL  IN  PER- 
SPECTIVE. 

PLATE     XLV. 

445.  It  was  stated,  in  the  preliminary  instructions  relating  to 
perspective  drawing,  that  the  perspective  dimensions  depend  on  the 
position,  both  of  the  point  of  sight  and  of  the  object,  from  the  plane 
of  the  picture,  which  is  necessarily  limited  in  size. 

In  the  perspective  delineation  of  one  or  more  objects,  we  should 
r  insider,  not  only  from  what  distance  the  object  should  be  viewed, 


but  also  at  what  height  the  eye,  or  (he  horizontal  line,  should  bo 
placed.  In  the  example  selected,  we  have  supposed  tin-  point  of 
sight  to  be  placed  at  the  height  of  a  man's  eye  ;  but  it  is  evident 
that  this  height  of  horizon  is  not  invariable.  It  depends,  more  or 
less,  on  what  part  of  the  object  we  wish  to  develop  more  particu- 
larly in  the  perspective  representation.  Thus,  for  a  machine  of  but 
little  height,  the  point  of  sight  should  be  lower;  whilst  it  should, 
in  all  cases,  be  at  a  sufficient  height  to  enable  the  spectator  to  take 
in  the  entire  object,  without  changing  his  position. 

In  architectural  subjects,  the  horizontal  line  should  never  be 
taken  at  a  less  height  than  that  of  a  man's  eye;  whilst,  in  general, 
a  good  effect  may  be  anticipated,  when  the  distance  of  the  spectator 
from  the  picture  is  equal  to  about  one  and  a  half  times,  or  twice 
the  width  of  the  paper,  provided  there  is,  at  least,  as  great  a  distance 
between  the  plane  of  the  picture,  and  those  parts  of  the  object 
which  are  nearest  to  it.*  Taste  and  practice  in  drawing  in  perspec- 
tive will  be  the  best  guides  in  the  choice  of  the  dispositions  leading 
to  the  happiest  effects. 

We  have  at  t  I',  figs.  1  and  2,  Plate  XLIV.,  indicated  the  position 
assumed  for  the  plane  of  the  picture,  which  is  supposed  to  be  brought 
into  the  plane  of  the  diagram  in  fig.  5,  Plato  XLV. 

The  point  of  sight,  agreeably  to  the  recommendation  we  have 
given,  is  supposed  to  be  placed,  with  reference  to  the  picture,  at  a 
distance  equal  to  about  twice  the  width  occupied  by  the  machinery 
of  the  mill  in  the  vertical  projection.  It  does  not  lie  within  the 
limits  of  the  paper  in  the  geometrical  projections,  Plate  XLIV.; 
but  it  is  projected  into  the  plane  of  the  perspective  picture  in  the 
point,  r',  tig.  5. 

In  laying  out  the  main  design  of  this  perspective  picture,  we 
must  commence  by  finding  the  positions  of  the  axial  lines  ot  all 
the  columns,  iron  shafts,  horizontal  and  vertical,  and,  in  general, 
of  all  symmetrical  objects.  Thus,  through  the  points,  ],  2,  3.  4, 
&c,  fig.  1,  we  must  draw  a  series  of  visual  rays,  converging  to  the 
point  of  sight,  and  cutting  (he  projection,  I  l1.  of  the  plane  of  the 
picture,  in  the  points,  1",  2",  3",  4".  &c.,  which,  in  the  picture 
itself,  fig.  5,  Plate  XLV..  are  represented  by  the  points,  1',  2',  3',  4', 
&c. 

The  vertical  lines,  drawn  through  each  of  these  points,  will  be 
the  axial  lines  sought.  We  next  obtain  the  perspective  of  the 
objects  situated  nearest  to  the  picture  plane,  as  the  column,  .x.  for 
example.  This  column  being  very  near  the  plane  of  the  picture, 
and  the  visual  rays  tangential  to  each  side  of  the  cylindrical  sul- 
face,  being  both  very  much  inclined  to  Iho  same  side,  its  diameter 
in  its  perspective  plane  seems  proportionately  greater  than  it  is 
in  reality ;  but  this  is  corrected  by  the  obliquity  wilh  which  this 
part  of  the  perspective  picture  should  be  viewed.  For  it  must  he 
borne  in"  mind,  that  all  perspective  pictures  must  be  viewed  from 
the  single  and  precise  point  of  sight  in  relation  to  which  they  are 
drawn ;  otherwise,  the  pictures  will  have  an  untrue  and  distorted 
appearance. 

We  next  determine  the  perspective  of  the  columns,  v,  the  axes 
of  all  which  are  situated  in  a  plane  perpendicular  to  the  plane  of 


•  We  do  not  see  the  force  of  this  remark,  for  why  should  not  a  perspective  repre- 
sentation be  lirawn  full  size,  or  even  to  a  larger  scale?  In  one  case,  the  object  roust 
be  supposed  as  close  to  the  plane  of  the  picture,  and,  in  the  other,  as  between  it  ALd 
the  point  of  sight.— Translator  ask  Editor. 


THE    I 


uW  sirtar.     ►   itat  they  «iU  dhatafa*  gradual!*  ill  bright,  being 
iaah*<t  byaroa^of  faeAeonTwgiogto  I 

•  IMM,  that  when  the  perspective  of  the  first  column  baa 
heea  -*J^— <.  it  w>ll   be  aafict.  nt  tu  draw  through  the   principal 

■  the  nv  uljm.-v  and  other  parte,  a  - 
mgia  the  nasal  >>birh  will  give  the  ptrspert: 

!!■«..  of  the  corresponding  points  on  the  other  columns,  together 

N.ir  heights. 

■f  each  of  the  runner  shafts, 
the  poller*,  and  other  detaii-  in  the 

vertical  plane,  p— ing  t 

X  1.1  V.. 

mi  eoBaaa^BBtJ]  NfjresMted  in  r«  r»i»vt.ie  bj  the  vertical   inea, 

.1  t<i  find  thi   ; 

- 

■ 

or  Hani. - 

which,  however,  are  p 

apez  of 

- 

by  lines 
.f  that 

■ 

them  ha« 

- 

h  Mipfxirt  the 

■ 

- 

■  ion   in 

■ 

strict  accordat  ,   |^y  (],,wn   il 

treating  of  aha  i-ing. 


NOT1  •  r    IMl'l!o\  i:  M  KN  I 

PLOUB.MILl 

By  far  the  I-  -t  millstones  used,  in  this  or  any 
an-  tiLv.-  -tones  from  t' 

■ark.  and  taming  out 
-.  than  any  oil. 
in  composition,  and  a) 

are  now  •  ry  part  of  tl>  :;sh  sys- 

takerj  to 
extract  • 

i  faces  being  -  !  u[»>n»  instead 

irtificial  furrows.     The  pm. 

n  such  way  a- 
grinding  action  without  interfering  with  th<  ,-t,  is  an 

invention,  introdao  I  in  :,_•■      II 

uncertainty  at;- 

poo  the 
Imilding  up  together  small  fragments  of  - 
i    rdi  ■  --.  so  as  :•■  inson  a  good  grinding  -ml"... .-  throughout — thia 

l  attainable  in  larpe  masses,  a 
parts  fr-  makers 

- 

and  as  the  manufacti.r 

.   n  to  bo 
.<!1  carefully  at 

;  and 

round  " 

i,  thai 

Uiron,  put  on  hot,  so  as  !•• 
Tin-  J •• 
the   fur: 

■ 

■ 
!  luces  annus' 

and  an  i  I 
■ 

- 

ind  an  important  application  in  the 
grindin. 
departure 

1 


BOOK   OF   INDUSTRIAL  DESIGN. 


into  a  series  of  infinitely  short  lengths,  he  proposed  to  take  a  more 

obtuse ic  Cor  carh  larger  portion,  and  in  such  progression,  that 

it  would  require  equal  pressure  for  every  portion  of  the  surface  to 
cause  a  uniform  sinking  of  the  plus  '"  the  course  of  wear.  The 
contour  thus  obtained  is  of  a  peculiar  curve,  as  shown  in  fig.  1. 
The  main  feature  of  the  generating  curve  for  such  a  surface,  is  the 
equality  of  all  tangents  drawn  from  the  curve  surface  to  the  axis; 


hence  the  use  of  the  simple  instrument  illustrated  by  fig.  2.  This 
contrivance  consists  merely  of  a  straight  brass  wire,  A,  jointed  at 
one  end  by  a  pin  to  the  upper  surface  of  a  small  wooden  slider,  b, 
which  is  hollowed  in  the  centre  to  receive  the  tip  of  the  finger  in 
drawing  a  curve.  A  small  drawing-pen,  c,  ingeniously  formed 
out  of  a  slip  of  steel  bent  over  the  wire,  a,  and  screwed  to  a  brass 
bush,  so  as  to  form  two  broad  nibs,  is  arranged  to  slide  from  end 
to  end  of  the  wire,  being  adjustable  at  any  point  by  stiff  friction, 
caused  by  a  spring,  which,  fitting  a  groove  in  the  wire,  retains  the 
vertical  position  of  the  pen.  In  drawing  a  curve,  the  rod  or  wire 
carrying  the  pen  is  set  at  right  angles  with  the  slider,  b,  which  is 
drawn  in  a  right  line  along  the  edge  of  a  ruler,  whilst  the  wire 
carrying  the  pen  is  left  to 
find  its  way  from  its  initial 
angular  position,  to  that  of 
a  line  in  the  same  plane  as 
the  slider ;  and,  in  doing 
this,  the  pen  describes  the 
curve  we  have  represented. 
Fig.  3  is  a  vertical  section 
of  a  millstone  arrangement 
on  this  system,  showing 
how  the  gradual  variation 
of  the  curvature,  in  rela- 
tion to  the  increasing  dis- 
tance of  the  parts  from  the 
centre  of  motion,  equalizes 
the  rubbing  pressure  iu  the  most  perfect  manner.    The  same  s"ketch 


also  shows  the  adaptation  of  the  principle  to  footsteps,  together 
with  a  new  system  of  lubrication  of  these  surfaces  so  liable  to 
extreme  abrasion.  The  oil  supply  is  kept  in  an  elevated  vessel,  A 
whence  a  pipe,  B,  proceeds  downwards  to  the  footsteps,  upon 
which  a  pressure  is  thus  constantly  kept  by  the  oil  column,  a  stop- 
cock being  introduced  to  regulate  the  supply. 

Mr.  Schiele  now  makes  independent  or  self-contained  flour-mills 
of  this  kind,  of  such  simplicity  and  compactnoss,  that  four  com- 
plete mills,  or  sets  of  stones,  placed  together,  may  be  worked  in  a 
room  10  feet  square;  a  single  shaft  driving  the  set,  from  the  cen- 
tre, by  means  of  a  horizontal  band-pulley,  from  which  endless 
bands  pass  to  corresponding  pulleys  on  the  spindle  above  the 
upper  stone.  In  mills  of  this  kind,  when  by  wear  the  runner  has 
sunk  three  inches,  the  adjusting  screws  of  the  steps  arrive  at  the 
end  of  the  3-inch  traverse  allotted  to  them.  The  runner  is  then 
lifted  from  its  seat,  and  the  thin  end  is  shortened  to  this  amount. 
This  plan  of  renovation  may  be  repeated  twice,  thus  allowing  for 
12  inches  wear  in  a  2G-inch  runner;  and  the  stones,  so  reduced, 
are  still  valuable  for  smaller  mills. 

The  peculiar  portability  of  these  mills  is  a  valuable  feature  of 
improvement.  No  fixtures  are  required,  as  the  weight  of  the  parts 
insures  steadiness  in  working.  Perfect  uniformity  of  wear  in  the 
grinding  surfaces  is  attained  by  the  use  of  the  curved  face  ;  and 
the  expensive  dressing  necessary  in  flat  stones  is  here  entirely  ob- 
viated, as  the  occasional  grinding  of  hard  substances  roughens  the 
faces  to  an  extent  sufficient  for  grinding  all  the  softer  materials, 
which  gradually  smooth  down  the  faces. 

Any  of  the  materials  ground  in  common  mills,  and  u  any  which 
the  latter  cannot  properly  act  upon,  are  capable  of  .eduction  in 
these  mills.  For  flour  and  other  finely-ground  substances,  a  few 
air-channels  are  formed  down  the  face  of  the  runner.  Their  best 
speed  is  only  half  that  of  common  stones;  and  the  inventor  states 
that  his  experimental  results  go  to  show  that  a  two-feet  runner 
produces  as  much  flour  as  a  four-feet  tlat  millstone,  the  power 
required  being  a  minimum.  If  the  stones  run  empty,  no  contact 
can  take  place,  therefore  there  is  no  firing,  nor  does  a  variation  in 
the  feed  or  speed  cause  any  difference  in  the  relative  position  of 
the  stones,  on  account.of  the  firm  and  steady  revolution  on  the 
curved  pivots.  The  antifrictional  qualities  of  these  pivots  are 
pretty  well  elucidated  by  the  fact  of  the  very  minute  consumption 
of  oil  upon  them. 

The  "  Ring  Millstone,"  invented  by 
Mr.  Mullin  of  Gilford,  Ireland,  is  pro-  Fi»-4- 

posed  as  the  means  of  securing  four 
special  advantages — economy  in  ma- 
nufacture, simplicity  and  effective  ven- 
tilation, increased  production  of  meal, 
and  a  saving  of  labour  in  repairs.  Fig. 
4  is  a  vertical  section  of  the  stone,  and 
fig.  5  is  a  corresponding  plan.  The 
"  eye,"  a,  is  made  excessively  large  in 
proportion  to  the  stone's  diameter,  ex- 
ceeding, indeed,  half  the  latter  dimen- 
sion.    This   increased   area  admits   a 

greater  volume  of  air  than  is  usual,  and  this  air,  coming  in  contact 
with  the  more  rapidly  revolving  portion  of  the  stone,  is  passed 


admits  of  thr  foraasliua  of  thr  •>  the  ordinary  I 

of  1«.Iii.,'  f,ir-..»«   for  the  il.K'.nhuli  n  of  tin  air  o\.  r  the  grin.lirig 
anrbm.  aod  thu»  ro^rr  grain 

..rea  of 
«.  .  •.  .  .•  -:  -..  at  •.:,.■  r.n!.T,  ili.  operation  of  (Ironing  i-  ob- 
i 

.   a  pcr- 
nx-a'-le   anafaMMO,  r.-ij^.'.  ■    •!   Jn-vun;'»i;rial   portion  uf  the   flour 
during  lh.-  actual    grit 
■ 

which  i»  liU-raU-d  jo- 
in   tlie    lower    si.. in-,    aii.l    tin. 
coarser  pa." 

1   from   tin-   final  on.  • 

tin.   npper  atone,  n  - 

- 

thf  direction    of   tli. 

down   upon  thu 

1  the 

me. 

of  ■  Bopr  throngfa 

I   that  lie  can 

-  from  ordinary  wheat,  from  one  to 
• 
I 

U 

•  •  each  pair  of 
ico-printing  m  i 
Gridusl  small  el  II 

F.».  7. 


_ 

e               1 

1 

,_ 

n 

;.  which  form*  the  a\i*  of  the  npper 
I  f  the  rode,  c,  with 

■| 
i  with  a  fly-wheel,/,  whirl, 
o»'t  for  driving  floui  ere  ia   alio  an 


. 

i ;  and 
from  tl>. 

for  the  lower  and  of  U  arnica 

i 
longitudinally  by  the  bearing  in  the 
I,  /.  hut  only  laterally  :  ami  there  in  a  hard, 
in  that  lower  and,  whi       I  I  at  tho 

I 
■ 
■nd  ill. 

•  ilt,  which,  I-  ■  nut  fitted  opon  the 

■crew  tl 

end  of  the  lever,  and  thus  the  upper  milli 
to  the  inl  from  the  lowi  It  fa 

th«>  vertical  movement  which  is  occasionally  required  t"  I* 

-. ./.that  tin'  ronnectii  \  I 

to  the  piston-rod  by  nonrenal  joints. 

!  by  tho 

both  i  nda  of  the  cylinder,  «.  and  connecting  it  at  •  . 
with  the  abaft,  <.'.  of  the  upper  mill-:  \  to  tin-  pah;  of 

mill-ton  •  n  that  side  of  the  stasm-engi 

it  should  be  di  lime  to  work  only  one  of  the  upper 

the  other  maj  ' 
ereto. 

ild  nir  with  tho  grain 
tween  ll  of  the  moot  im- 

portant of  the  modern  improvementa  in  grin  1 

anrfacea  are  Ihm  increas- 

ed, whilst  the  quality  of  Boor  ia  very  superior  to  that  produced  in 
fiie  old  way.    It  ia  thin  feature  which  bolda  a  prominent  place  in  a 
invention  by  Mr.  J.  C  < .      •  .w. 

-  of  our  angravin  •-  ia  a  w  rtscal   - 
millstone  arrangemi  nta, 
with  the  Foi 

this  par] he  asea  two  grain   feed-pipes, 

wards,  like  a  forked  i  m  the  narrow   fa 

the  hopper,  n,  the  n  ■  pindle,  c, 

.;.  from  the  main  spindle,  Di  through  a  joint-hole 
in  thf  fork,  int..  the   main  un  from 

the  hopper.    After  diverging  downwards,  until   tiny  reach  tho 
npper  surface  of  the   fixed   atone,  a,  lha   two   I 
vertically  thron  dlreotly  through   lha 

upper  - 
tho  stone.    An  annular  portion  of  tho  under  surtsoe  of  tl 

through 
■  from  tin'  outer  aide  of  tin  a 

twei  n  the  two 

•    thfa    part,  For   the    I  I  M   grain   ami    air,  ami 

precluding  Un  oham f  the  i imencemenl   of  the  grinding 

nation,  before  the  air  has  full] 

lha   npper  fixed   atone,  between  the  two 
.  over  »iili  :i  •  paaaed  over  the  feed-spindle, 

adjustment  at  the  aye 


BOOK    OF    INDUSTRIAL   DESIGN. 


as  a  valve.  The  grinding  surface  of  the  lower  running  stone,  H, 
is  perfectly  Sat  throughout,  and  its  eye  at  the  grinding  level  is 
covered  over  hy  a  metal  plate,  f,  with  a  ventral  aperture  round 


the  feed-spindle,  G,  for  the  passage  through  of  a  portion  of  the 
air.  In  this  way,  part  of  the  air  may  be  discharged  at  the  eye  of 
the  upper  stone,  and  part  down  through  the  eye  of  the  runner 
beneath,  whilst  the  main  body  of  the  air  goes  along  with  the 
grain,  and  is  discharged  with  the  grained  material  at  the  periphery 
of  the  stones.  By  this  contrivance,  the  entire  surface  of  both 
stones  is  kept  encircled  by  a  constantly  changing  air-bath  or 
current,  for  the  air,  escaping  at  the  eye  of  the  upper  stone,  is 
directed  by  the  valve  disc  over  its  entire  surface,  whilst  that  from 
the  bottom  of  the  lower  eye  passes  over  the  whole  bottom  surface 
of  the  runner,  between  it  and  the  bottom  base  plate,  i.  This  has 
a  ventilating  effect ;  for  on  the  upper  edge  of  the  iron  casing,  j, 
which  surrounds  the  lower  running  stone,  and  supports  the  upper 
fixed  stone,  is  placed  an  annular  disc  of  wire-cloth,  K,  covering 
over  the  annular  space  left  between  the  periphery  of  the  stones 
and  the  interior  of  the  casing.  This  wire-cloth  stands  a  short 
distance  above  the  level  of  the  grinding  surfaces,  and  from  its 
periphery  a  light  wooden  casing,  l,  springs  upwards,  surrounding 
the  upper  stone,  and  bevilled  inwards  at  some  distance  above  the 
stone's  surface.  Thus  there  is  a  current  of  cold  air  passing  from 
the  running  eye  up  outside  the  stone  and  inside  the  casing. 
There  it  meets  the  heated  current  from  the  grinding  surfaces  at 
right  angles ;  and  breaking  this  heated  current,  whatever  grained 
material  is  held  in  suspension,  falls  back  within  the  bottom  casing, 
whilst  the  heated  air  passes  off  through  the  wire-cloth,  again 
meeting  at  right  angles  with  a  cool  current  from  the  upper  side  of 
the  top  stone,  which,  in  conjunction  with  the  bevilled  top  of  the 
upper  case,  still  further  separates  the  suspended  flour,  and  aids 
the  ventilation.  Another  modification  of  stones  relates  to  the 
combination  of  three  or  more  separate  stones,  instead  of  two.  as 
hitherto  used.  In  this  plan,  which  is  represented  in  fig.  9,  the 
central  stone,  a,  is  the  runner,  the  upper  and  lower  ones,  n,  c, 
being  fixed,  so  that  the  grinding  is  performed  both  between  the 
under  surfaeo  of  the  upper  stone  at  D,  and  the  upper  surface  of 


the  central  runner,  and  between  the  under  surface  of  the  latter 
and  the  upper  surface  of  the  bottom  fixed  stone  at  E.  The  grain 
is  fed  through  the 
pipe,  F,  into  the 
hopper,  G,  through 
the  adjustable  feed- 
passage  into  the  pipe, 
H.  Hence  the  supply 
for  the  upper  grind- 
ing surfaces  passes 
out  by  the  inclined 
lateral;opcning,  i.into 
the  hollow  space,  J, 
in  the  upper  stone, 
forming  the  lower 
part  of  the  eye  there- 
of. Here  it  falls  on 
to  the  disc,  K,  and  is 
directed  to  the  grind- 
ing   surfaces.      The 

supply  of  grain  for  the  lower  or  secondary  grinding  action  passes 
out  at  the  bottom  of  the  pipe,  H,  into  the  eye  of  the  runner,  A, 
and  thence  proceeds  to  the  grinding  surface.  The  upper  stone  is 
supported  by  side  brackets,  these  brackets  being  carried  on  the 
lower  annular  casing,  l,  bolted  down  to  the  floor.  The  bottom 
stone  is  sunk  in  a  casing,  m,  recessed  into  the  floor  or  platform, 
being  steadied  late- 
rally by  an  annular 
piece  of  metal  level 
with  the  floor,  whilst 
it  rests  on  adjusting 
bolts,  N,  beneath. 
The  spindle,  driven 
by  gearing  from  be- 
low, rests  in  an  ad- 
justable balanced 
footstep.  It  is  fitted 
to  the  runner  by  a 
Ryne,  made  on  the 
"  balance  "  principle. 
The  top  of  the  spin- 
dle is  spherically 
shaped,  as  at  o,  be- 
ing passed  through 
the  collar  disc,  p, 
and  fitted  into  a 
spherical  recess  in 
the  under  side  of  the 
Ryne,  Q,  connected 
to  the  stone,  a.  In 
this  way,  as  the  con- 
nection between  the 
spindle  and  the  stone 
is  entirely  formed  by  this  ball  and  socket,  no  derangement  can  ansi 
from  the  spindle  and  runner  getting  out  of  truth. 

Fig.  10  is  a  vertical  section  of  the  "balance  Ryne,"  on  a  large* 


araie.     a  m  lb*  ban*-  [Jav.  and  •  lb*  loner  running  «!•■:.• 
fro-n  »l..«r  by  Ibe  maia  aeaadle,  I,  which  paaaga  down  t!. 
cawtr*  of  Iba  k!,u.'»kr  tube*  of  tba  d-cd-bopper,  and  trrnunatra 
la  a  o 

lb*  diae  pier*,  D,  wbirb  baa  famed  upon  Ibe  epn" 
►    ••*  .   »  .   i  .  r   »•   |.  piec*.  readag  in  a  bfaai    ..-r  .  I 

I    . 

:nd  arranged   I 
■ 

of  Iba  H 

ruinate  in  an  annular 

.: 
•<  an    u|'|it  C"l!ar  \>\»<h  it.  I 
T     -  pass  at 

.  and  finally   I  which 

. 

teral  adjustment,  and 

truth   with  the 

- 
■ 

I 

-  when 
»  [idle,  ami  thus 

..  o,  as  may  b. 

I  and  a 

■ 

1 

of   ill..- 

•  •t*  the 
I  -rk  of 

Iheae  maker*. 


Ki  l.r.s  AND  PRACTICAL  DATA 
W01 

.r  nulla,  the  .i 


on  V  ■ 
is  aoax-  inaged  eatabhahnienU  in  and  around  Pari*, 

■ 

!  in   this  ma-  I  al  it  rr. 

quirea  ai  -.ilagrain- 

I-  r   hour.   Of  ■ 
gntuifm •».     )u 

work,  n  -,  but  also  all  i  pparataa 

mill. 

from  15  ' 

or  51  kDogrami 

:  .u,  1  bulling 
-     • 

■ 
of  15  horsea  power,  w<  -.nix  pairs  ol 

ring  apparatus  and  c  W 

r,  that  iu  this  i 
- 
is  mail. 

-' 

an  actii< 

.  . . ii- 1  as  mucl. 

In  ni 

- 
of  Bur^unilv  al  ills  are 

■ 

- 
-i-cunds 
M  mills. 
The  p 
■lihoogl 

ni.  that 
uniler  thi 

of  75 

i  actual  gain,  as  far  as 
it  ;  nnd  it  may  be  said,  indeed,  that  with  a  powar 
of  four  boraaa,  from  100  to  lot  kilo^r. 

- 
-    :i  and  around  I'ari.t,  the  san.- 
■ 

n  which,  as  we  have 
said,  a  it, 

■ 

apparatii- 

I  of  wheal 


BOOK   OF   INDUSTRIAL   DESIGN. 


169 


ground  per  horse  power  per  hour.  In  fact,  experimental  investi- 
gations have  shown,  that,  with  a  steam-engine  of  from  24  to  25 
horses  power,  working  seven  pairs  of  stones  of  13  m.  in  diameter, 
17,374  kilog.  of  wheat  could  he  ground  in  the  24  hours.  This 
corresponds  to  a  power  of  3|  horses,  and  103-4  kilog.  of  wheat 
ground  per  pair  of  stones,  or  to  29-5  kilog.  per  horse  power  per 
hour. 

We  may,  therefore,  deduce  from  the  preceding  results : 

First — That  with  an  effective  power  of  one  horse  (or  75  kilo- 
grammes raised  one  metre  high  per  second),  a  mill  should  grind  a 
minimum  of  20  kilog.  of  wheat,  and  a  maximum  of  30  kilog.  per 
hour. 


Second— That  the  minimum  quantity  applies  to  mills  wbieh  are 
worked  for  commercial  purposes,  and  particularly  for  the  Parisian 
consumption,  producing  the  greatest  possible  quantities  of  the 
higher  qualities  of  flour. 

Third— That  the  medium  quantity  (of  from  25  to  26  kilog.  per 
hour)  is  that  produced  by  mills  likewise  worked  for  commercial 
purposes,  but  making  a  greater  quantity  of  second  quality  flour, 
such  as  those  at  Lyons  and  other  places. 

Fourth — Finally,  that  the  maximum  quantity  corresponds  to  the 
produce  of  those  mills  which  only  grind  the  coarser  qualities,  and 
in  which  the  cleansing  and  dressing  mediums  are  very  simple. 


TABLE  OF  THE  POWER  REQUIRED,  THE  QUANTITY  OF  WHEAT  GROUND,  AND  THE  NUMBER  OF  PAIRS  OF  STONES, 

WITH  THEIR  ACCESSORY  APPARATUS. 


Effect 

ve  Force  in 

Quantity  of  Wheat  ground  in  kilogrammes  per  hour. 

Nu 

nber  of  Pairs  of  Stones. 

Horses 

power. 

k.  m. 

Minimum. 

Medium. 

Maximum. 

Minimum. 

Medium. 

Maximum. 

1 

75 

20 

25 

30 

1 

1 

J 

2 

150 

40 

50 

60 

1 

1 

J 

3 

225 

60 

75 

90 

1 

1 

] 

4 

300 

80 

100 

120 

1  to    2 

1 

1 

5 

375 

100 

125 

150 

2 

1  to    2 

1  to    2 

6 

450 

120 

150 

180 

2  to    3 

2 

1  to    2 

7 

525 

140 

175 

210 

2  to    3 

2 

2 

8 

600 

160 

200 

240 

3 

2  to    3 

2 

9 

675 

180 

225 

270 

3  to    4 

3 

2  to     3 

10 

750 

200 

250 

300 

4 

3 

2  to    3 

12 

900 

240 

300 

360 

4  to    5 

4 

3 

14 

1050 

280 

350 

420 

5 

4  to    5 

4 

16 

1200 

320 

400 

480 

6 

5 

4  to    5 

18 

1350 

360 

450 

540 

6  to    7 

6 

5 

20 

1500 

400 

500 

600 

7 

6  to    7 

5  to    6 

22 

1650 

440 

550 

660 

8 

7 

6 

24 

1800 

480 

600 

720 

9 

8 

6  to    7 

26 

1950 

520 

650 

780 

10 

8  to    9 

7 

28 

2100 

560 

700 

840 

11 

9 

8 

30 

2250 

600 

750 

900 

12 

10 

8  to    9 

32 

2400 

640 

800 

960 

12  to  13 

10  to  11 

9 

34 

2550 

680 

850 

1020 

13 

11 

9  to  10 

36 

2700 

720 

900 

1080 

14 

12 

10 

38 

2850 

760 

950 

1140 

15 

12  to  13 

10  to  11 

40 

3000 

800 

1000 

1200 

16 

13 

1 1 

45 

3375 

900 

1125 

1350 

18 

15 

12  to  13 

50 

3750 

1000 

1250 

1500 

20 

16  to  17 

14 

55 

4125 

1100 

1375 

1650 

22 

18 

15  to  16 

60 

4500 

1200 

1500 

1800 

24 

20 

17 

65 

4875 

1300 

1625 

1950 

26 

21  to  22 

18  to  19 

70 

5250 

1400 

1750 

2100 

28 

23 

20 

75 

5625 

1500 

1875 

2250 

30 

25 

21  to  22 

80 

6000 

1600 

2000 

2400 

32 

26  to  27 

85 

6375 

1700 

2125 

2550 

34 

28 

24 

90 

6750 

1800 

2250 

2600 

36 

30 

25  to  26 

95 

7125 

1900 

2375 

2850 

38 

31  to  32 

27 

100 

7500 

2000 

2500 

3000 

40 

33 

28  to  29 

This  table  is  calculated  upon  the  conclusions  preceding  it,  and 
gives  at  sight,  on  the  one  hand,  the  quantity  of  wheat  which  can 
be  ground  by  a  given  effective  power,  and,  on  the  other,  the  ap- 


proximate number  of  pairs  of  stones  which  may  be  erected  when  it 
is  desired  to  fit  up  a  mill  with  a  determined  power. 

It  is  easy  to  see,  from  this  table,  that  the  number  of  pans  ot 


rfnom  rnriee  in  arvordaoea  » i:h  th*  three  Systran  ad  •[»!• 
h  Hi    i  th.  table  «.::!<»  somrirnt  guide  for  tb*  constru. 
low  mffl*,  whatn.-r  amy  be  the  description  of  prim*  mow  . 
ed.     It  BMt  be  remarked,  thai  iti»  moat  fre<ioeotly  upon  »uch  data 
that  the  number  of  stoors  ought  U)  be  determined,  when  an  oU 
rather  than  upon  tli. 

of  the  mill  which  pre* 

H  by  a  niill  or. 

known    ■ 

gr  four  pt^rs  • 
atnoea  of  1-3  m.  in  diameter  »  thcr  mills,  six, 

•••in  various  causes.     Thus  it 
will  be  understood,  th  •'  ■  '"  an  old  mill, 

t*  badh  ind  badly  arranged,  it  will  utilize  very  little 

of  the  deposable    force,  and  re,  only  give   out  an 

amount  of  work  uju 

large  Preach  stones,  with  large  eyes  but  ungrooved,  can  be  made 
I  little  or   much   at    ; 

in  fact, 
that  the  quantity  of  wheat  ground  by  a  pair  of  Urge  stones,  in  a 
Ml  ground  by  a  pair  of  small 
ataaaa, 

•  rence  to  thi-  .-i-.thtr  remark  to  Ik- 

ip~t«)  which  will  not  be  without  importance.     In  many  '■■ 
without  adopting  the  ! 
mills  established  on  a  ■ 

the  ma  lb*  bydrnalie  prime  morer, 

hare  been  im;  •  B  '-   sufficiently  advanta- 

and,  in  fact,  i:  •    more  with  a 

,  than  they  ban  I  producing  at  a  later 

■  ■i   l.y  appanttna  entirely  on 

the  constructor 

staining  worse  results  after  than  before  the 

It  niu»t  be  recollected,  that  when  i  French  mill  are 

improTed — that  fa)  to  m 
it,  and  a  good  - 

and  not  rncum  th  much  aiv.  -- 

kv  after  all,  when  taken  as  a 

than  the  English  mill  which  is  substituted  for  it — whoa 
with  the  same  amoun!  'lian  the 

latter,  although    this    latter  !.   became    the 

machinery  is  ■  and  better  adapted  for  working  in  a 

regular  and  continuous  man 

i»t  also  remark,  that  there  are  mi  -  stones 

•  f  from  14  to  15  m.  in  diameter,  at 

adopting  the  i  ral  details — that 

w  to  nay,  the  atones  are  grooved  and  dressed  in  exactly  the  same 
manner  as  those  of  1*3  m.  in  dian 

due*  n> ••  Ibjaj  the  Utter,  although  they  are  not 

,t  so  rapid  a  rati',  th.- 

1'iieee  larger  dimensions  may  have  the  advan- 
tage of  simplifying  the  machinery,  and  diminishing  the  number  of 


.  m  the  one  hand,  and  perhaps,  on 

■  -      It 

•   a  mill, 

-     .ral  pairs  of  stones  of  13  m.  in  diameter,  may  at 

utilized  with    - 
Again,  it  I 

drive  two  pairs  of  small  ttoi 
one  pair  ;  or  that  it  is  i  go  to  the  cx|- 

witfa  a  single  pair  i 
profitably  employed,  and  ti 

repairs,  and  keeping  iti 

V,  remarks  by  a  statement  of  l 

.  mills,  of  different  epochs  : — 

1 1  rtt  Statement  of  Produce,  obtained  from  an 
belo-.ioing  to  Jf.  Bn<  •.  «o«r  no  longer  in  mU 

. 

Wheat  flour .6*1 

Flour  separated  from  the  oatmeal,  .let        "        ..    ll  A" 

•       ..  I  i"  =  »«  pel  '"■' 

"  3rd  and  4th.      "        ..  «J 

Coarse  bran SO  fail 

•• 

Coarse  meal,  "  8  |   — 

•■•  50                  "                ...  4 J 
I  loss =    2 

General  total, 

-  rend  Statrmmt  <f  Produce , 

It)  of  \VI„at,  i  U  liilog.,  obtained  from  a  Mill, 

on  the  Ennlith  eyitem,  near  Paris. 

Flour,  1st  and  2nd  quality,.  . 

Srdqualiti l,MOl=t-| 

"     4th     ••    '  :.•''*•■•  1 

sifiiuLT- «,8oo     =    •: 

•  5       " 

Pfaeta and  loat 16,070     =»•«      " 

al  total, fclf,in  kilog. 

Butheh)  of  Wheat,  Wtifki»$  11,8 

:-!  quality B,«60  =  ""  !  ■ 

tta  ns  %    ■ 

••      Irdend  Ufa 411  =    4      " 

Various  products, MM  es  M 


S    1  W.MILLS. 

iiT    Bkrw-mflk  may  be  dhinad  into  Iwo  dk« 

Dam.lv.  those   in   which  the  saws  have  a eontfainoai   mot 
mom  in  which  the  motion  ■  rocippicatory. 

The  first  class  comprises  not  only  circular  saws,  but  BH 


BOOK   OF    INDUSTRIAL   DESIGN. 


which  consist  of  a  thin  flexible  steel-plate,  passed  round  two  drums 
or  pulleys,  like  an  ordinary  pulley-belt. 

The  second  class  comprises  straight  saws,  acting  vertically  or 
horizontally,  or  sometimes  slightly  inclined. 

We  shall  here  give  the  notes  of  some  experiments  upon  asawing- 
machine,  having  several  saw-plates  arranged  side  by  side  in  a  frame, 
weighing  altogether  nearly  400  kilog. 

The  power  expended  by  the  prime  mover  was,  for  -161  sq.  m.  in 
area,  sawn  through  per  minute,  in  dry  oak,  3-7  horses  power ;  and 
4-5  horses  power  for  an  area  of  '131  sq.  m.  sawn  through  per 
minute,  in  oak  that  had  been  cut  four  years.  In  these  instances, 
four  saw-plates  were  worked  at  once,  which  gives  for  each  saw- 
plate,  in  the  first  instance,  -925  horses  power  per  plate  ;  and,  in  the 
second,  1-125  horses  power. 

The  width  of  the  set  of  the  saw  is  ordinarily  3  to  4  millimetres 
at  the  outside. 

A  reciprocating  saw,  making,  on  an  average,  120  strokes  per 
minute,  with  a  length  of  stroke  equal  to  -6  m.,  the  cranks  being 
•3  m.  iu  radios,  passes  in  a  minute  through  a  space  equal  to 

120  x   2  x    6  —  144  metres  ; 
or, 

2-4  m.  per  second. 

Now,  with  such  a  stroke,  we  can  saw  through  a  thickness  of 
from  50  to  60  centimetres,  and  even  more.  In  taking  the  lower 
of  these  two  dimensions,  the  work  obtained  per  minute,  with  an 
advance  of  2  millimetres,  is 

120  x  -002  x  -5  =  -12  sq.  m., 
for  the  area  sawn  through,  measured  upon  one  side  only. 

This,  per  hour,  is 

•12  x  60  =  7-8  sq.  m. 

WORK   GOT   THROUGH,  WITH  A    LONG    SAW,  BY   TWO   MEN. 

448.  Two  men,  giving  on  an  average  50  strokes  per  minute,  can 
go  on,  without  stopping,  for  3  or  4  minutes.  Allowing  that  they 
stop  every  30  seconds,  or  half  minute,  the  stroke  of  their  saw  being 
•975  m.,  the  entire  length  of  the  plate,  13  m.,  they  will  saw  through 
a  length  of  '92  m.  in  7  minutes.  This  gives  for  the  area  sawn 
through— 

•92  x  -315=  -2898  sq.  m. ; 
or,  per  minute, 

•2898  -4-  7  =  -0414  sq.  m. 

Thus,  the  work  of  these  two  men  is  very  nearly  equal  to  that 
of  one  of  the  saw-plates  in  the  sawing-machine  first  described,  which 
requires  a  force  equal  to  one  horse  power.  This  difference  may 
easily  be  accounted  for,  when  it  is  recollected  that,  in  the  sawing- 
machine,  a  considerable  part  of  the  motive  power  is  expended  in 
overcoming  the  friction  of  the  various  moveable  parts,  through 
which  the  motion  is  communicated  to  the  saw-frame ;  whilst,  in 
manual  sawing,  the  power  is  applied  directly  to  the  saw,  and  the 
frame  is  always  a  very  light  affair,  especially  as  compared  with  that 
in  the  machine. 

In  a  manually-worked  saw,  such  as  we  have  alluded  to,  the 
teeth  are  '013  m.  apart,  so  that  75  teeth  come  into  action  during 
the  stroke  of  -975  m.  The  depth  of  these  teeth  is  -0065  m. ;  that 
is  to  say.  half  their  pitch.     They  are  very  slightly  bent  to  each 


side,  and  the  workmen  chamfer  off  their  inner  edges,  alternately  on 
one  side  and  on  the  other. 

As  the  saw  only  acts  during  its  descent,  it  may  be  deduced,  from 
the  preceding  statements,  that  its  mean  advance  is 
■92  m.  -r-7  =  -1314  m.  per  l'j 
and  per  stroke  of  the  saw, 

•1314  -4-  50  =  -00263  m.; 
that  is  to  say,  a  little  above  2.'  millimetres.     This  advance  is  very 
nearly  the  same  as  that  ordinarily  given  to  a  machine-saw,  when 
sawing  oak. 

VENEER-SAWING    MACHINES. 

For  veneer  saws,  which  generally  work  upon  hard  wood,  and 
which,  moreover,  produce  sheets  of  peculiar  thinness,  and  perfectly 
equal  and  regular  throughout,  it  is  obviously  impossible  to  advance 
through  the  wood  at  such  a  rate  as  is  customary  in  cutting  deal 
bulks  into  boards. 

The  velocity  of  these  saws  is,  perhaps,  greater  than  for  any  other 
purpose.  It  is  not  less,  in  fact,  than  280  strokes  per  minute,  and 
often  reaches  even  300  strokes,  which  is  more  than  double  the 
ordinary  velocity  formerly  adopted. 

If  the  saw  only  advances  through  mahogany  at  the  rate  of  \ 
millimetre  for  each  revolution,  the  length  sawn  through  per  minute 
will  be 

300  x  -0605  =  -15  m.; 
and  per  hour, 

•15   X   60  =  9  metres. 

If  the  width  of  the  wood  be  40  centimetres,  the  area  sawn 
through  per  hour  will  be 

9  x  -4  =  3-6  square  metres; 
and  per  day's  work,  of  12  hours,  allowing  2  hours  for  grinding  the 
tools,  fixing  the  wood,  arranging  the  saw,  lubricating,  vie.,  the  total 
work  done  will  be 

3-6  x   10  —  36  sq.  m.,  sawn  through. 

We  may  remark,  that  the  actual  juice  paid  to  saw-mill  owners 
for  sawing  mahogany  is,  at  Paris,  generally  28  fr.  per  100  kilog., 
20  sheets  of  veneer  to  the  inch,  or  27  millimetres,  of  width  being 
given. 

It  is  scarcely  twenty  years  since  the  time  that  10  francs  per  kilog., 
or  1,000  francs  per  100  kilog.,  was  paid  for  this  description  of  saw- 
ing; and  it  was  very  rarely  that  so  many  sheets  of  veneer  were  got 
out  of  the  same  thickness  of  wood.  This  immense  difference  will 
give  some  idea  of  the  effects  of  competition,  and  the  improvements 
continually  made  in  the  construction  of  machinery. 

CIRCULAR    SAWS. 

450.  Circular  saws  are,  without  question,  the  simplest,  and 
capable  of  the  greatest  number  of  applications  in  the  industrial 
arts.  They  are  employed  of  all  dimensions,  from  those  of  2  or  3 
centimetres  in  diameter,  to  those  of  1  metre,  and  even  more.  The 
smallest  and  weakest  are  generally  used  for  cutting  very  minute 
articles,  in  bone,  horn,  or  ivory.  In  the  machines  tor  cutting  the 
flat  sides  of  wheel-teeth,  we  find  circular  saws  employed,  of  from 
6  or  8  centimetres,  up  to  14  or  16  centimetres  in  diameter,  accord- 
incr  to  the  power  of  the  machine,  and  the  strength  of  the  teeth  to 


DRAUGHTSMAN'S 


V*  cat     la  earpaotry.  cataoeUnakinf,  and  coarh-makirv  i 
Stars  arc  .  ii. ;  ">  diameter.      ! 

rralar  sew.  may  be  r..i»«i.l.r.-.l  indispensable, 
dan,  and  alio  on  account  of 
the  prrfeclioo  of  their  wort     The  atwt  turd  in  theae  »•• 

aha  at  a 
rate  not  leaa  than  400  pat  minute,  and  in  some  cases 

xxrcsmtm  with  a  cisci-lar  saw,  -7  m.  is  diameter. 

J  sawn:  oak,  one  year  rift.  I 

— 


KmWi  of  ratolaoou  of  Ike  mm  par  *M 

Aim  m«i  ptr  eiitU 1*  «j  m 

i . — Kind  of  win  J  sawn  :  dry  deal,  in  pkufa 

■  — 

NumWi  of  nvolnuoM  of  th«  nw  ear  I' t44 

Araaaawu  in  1' -71«q.  «. 

These  Ibat,  for  ml  circular 

-  M  iiiiuli  work  a--  four  vertical  roctilinoar  aw»  in  tliu 
same  time,  and  with  tin-  vim.'  motive  power. 

It  must  b».  romariud,  thai  I 

product  of  the  depth  of  the  pi.  cc  b»  the  length,  sawn,  and  not  the 

Mim  of  the  two  boas  separated  bj  nsry  in 

calculating  WOOd. 


CHAPTEB    \iv. 
EXAMPLES  OF  FINISHED   DRAWINGS  OF  MACHINERY. 

BALAXCE     WATER     METER. 


EXAMPLE  PLATE  A- 


In  ap|  boon  for  the  in-truc- 

P  I1      .    ■  :-inari   in    Industrial    Design,  We  now 

•  :■  tails  of   the  finished 

I    foi         -     .'lidance. 

■  clmi  a  ol  can 
■n  the  part  of  the  draughtsman  who  oom- 

•-    and    fidelity    OD    the    part    of    the 

the  dvlineati  i 

.il  lights 

reying 
■  the  full  aixe  of  a  fluid  mi 

water,  or  as  moeh 

.  -vary  lor    thl 

It.  I 

..in,  »  brother  of  Mr.  E.   w    >  ■  ft  lin,  the 

."  both  uf  which  gen- 
well  known  to  the  reader!  of  theae  pages,  from 
Ui.  ir  in  us  to  physical  science  and  the  oonatractive 

art-. 

r"    is   of    the   rotatory   kind,  and   I 
i    with    the    v  Ing,  within    the    compass    of 

the  quantity  of 
aster  flowing  through  n  pipe,  with  equal  accuracy  at  all  p 
»nd  whbool  ttnaons  flow  from  the 

i  la  a  longilu  i  of  the  mater, 

•hOW  the 

I  ling  longitudinal 

ratun,  end  I  ■    whole  of   tbi 

aontaiiu  I  leal    eaat-iron    shall,  a.  having  pluin 


end  nangaa,  b,  for  bolting  it  in  the  line  of  the  water  supply-pips, 

and  a  short  cylindrical  box,  '  .  screwed   on    the    Up| 

the  Index  geai  -t  hollow  and  open  through- 

out, l.ut  with  three  projecting  annular  ribe  for  bori 
for  a  drawn  braaa  lining  tube,  D,  inaerted  for  the  purp 
securing  a  perfectly  uniform  area  throughout  the  waterway;  and 
within  this  waterway  are  planed  two  hollow  metal  drum-. 
ported  on  longitudinal  eel  in  the  axial  lii 

shell.    'I  tried  at  their  ontor  ends  in  lx 

g,  in  the  centres  of  the  fixed  b,  one  of  which  is  In 

Motion,  and  tl ppoaite  or  inner  spindle  bearings  are  in  i 

central  bracket  opposite  the  rib,  i.  of  tie 

dinal  half,  from  the  centre  line,  is  precisely  the  same  in  i 

tion.    The  coins.  11.  have  ca.li  projecting  spindle 

,  I   of   tile  shell,  where     IheV   .. 

cally  with  the  shell'e  uia,  bj  cross  Lars. ;,  in  -hallow  rii 

1   into  each  end  of  the  shell;   whilst  the  c< 
.    four    thin    radial    I 

lining.    The  inner  surfaces  of  theae  con.  nd  Lha 

slightly  convex  races  of  the  drums,  s,  project  s  little  way  Into 

1  iwn  on  the  ri  The 

drums,  K.  are  the  prime  motive  dotaj  - 

blades,  or  twisted  van.  s,  i„  sal  in  r.  i 

left-handed      Motion  i the    drum    BpL 

pinions,  »,  one  on   the  inner  end    of  each  -pin. He.      Bach    pinion 
te    .ToWII   Wheels.   >,  so    that   the  two 

are  oompelled  to  revolve  at  the  same  rate  In  opposite  directions. 

The   h.w.r  crown   wheel  is  simply  .  ihorl   stul-shaft, 

running  in  bearings  in  the  centre  I. racket,  I..  Ing  dm  rely  used  to 
coiin.et    the  t»o   pinions  on  the  lower  side;   whilst  tb< 

last    on    the   lower  end   OJ  ,'1'  Wted 


BOOK  OF    INDUSTRIAL  DESIGN. 


in  the  same  bracket,  and  passed  through  a  hole  in  the  side  of  the 
shall,  to  give  motion  to  the  counter  above.  The  special  object  of 
tills  application  of  the  second  crown  wheel,  is  the  neutralizing  the 
lateral  pressure  upon  the  drum  bearings,  in  the  transmission  of 
motion  from  one  drum  to  the  other;  aud  to  reduce  the  working 
friction  to  the  highest  degree  of  refinement,  the  total  weight  of 
each  drum  is  calculated  to  be  just  equal  to  that  of  its  bulk  of  tho 
fluid  surrounding  it.  The  water  enters  the  meter,  as  indicated  by 
the  duplex  spreading  arrow,  passing  through  a  coarse  grating,  P, 
intended  to  retain  pieces  of  wood  and  bulky  matters,  but  permitting 
the  water,  with  its  ordinary  impurities,  to  pass  through.  After 
passing  this  grating,  the  fluid  is  collected  towards  the  axis  of  the 
shell,  by  the  first  internal  conical  incline,  Q,  of  a  duplex  cone  piece 
inserted  within  the  shell,  aud  the  flow  is  then  directed  outwards 
by  the  second  reverse  cone,  R,  and  spread  uniformly  over  the 
quick  external  cone  of  the  pieces,  H.  The  object  of  this  direction 
of  the  fluid  is  to  prevent  partial  currents,  which  would  otherwise 
disturb  the  motion  of  the  working  drum  ;  and  as  water,  in  passing 
through  pipes,  sometimes  acquires  a  rotatory  motion,  the  conical 
block,  H,  is  armed  with  the  radiating  blades,  K,  to  direct  the  fluid 
in  a  line  parallel  with  the  axis,  prior  to  its  reaching  the  drums 
beyond. 

The  current,  thus  uniformly  spread  and  directed,  now  meets  the 
right-handed  screw  blades  of  the  first  drum,  e,  which  is  thus  caused 
to  revolve,  the  water  at  the  same  time  acquiring  a  certain  deflection, 
in  eonsequenee  partially  from  the  resistance  of  the  drum  to  rota- 
tion, and  partially  from  the  friction  of  the  fluid  against  the  surface 
of  the  revolving  drum. 

The  amount  of  this  deflection  or  "slip"  of  the  water,  varies 
with  the  velocity  of  the  current,  and  would,  of  course,  affect  the 
accuracy  of  the  measurement,  were  it  not  for  the  correcting  influ- 
ence of  the  second  or  left  serew-bladed  drum.  The  blades  on  this 
drum  are  of  precisely  the  same  pitch  as  those  on  the  first ;  and  as 
they  revolve,  they  meet  the  water  at  an  angle  so  much  greater  than 
occurs  at  the  first  drum,  as  is  due  to  this  angular  deflection. 
Hence  the  water  tends  to  drive  the  second  drum  faster  than  the 
first,  and  the  fluid  Buffers  twice  that  amount  of  deflection  in  the 
reverse  direction.  Hence  the  combination  of  the  two  drums  pro- 
duces a  powerful  water-pressure  engine,  upon  which  the  slight  fric- 
tion of  the  apparatus  exercises  no  appreciable  retarding  effect. 
Moreover,  the  friction  of  the  water  on  the  drum  surface  increases 
in  the  ratio  of  its  velocity,  and  the  result  is,  that  the  combined 
drums  move,  under  all  circumstances,  in  the  exact  ratio  of  the  cur- 
rent. The  outer  edges  of  tho  screw  blades  do  not  work  in  absolute 
contact  with  the  internal  surface  of  the  fixed  shell,  A,  but  no  water 
can  slip  through  this  way  without  impinging  on  the  vanes,  in  con- 
sequence of  a  slight  contraction  of  the  shell  between  the  two  drums. 
After  passing  both  drums,  the  water  is  again  directed  as  in  the  first 
instance,  and  passes  off  to  the  service-pipe  at  the  opposite  end  of 
the  shell. 

The  counter  or  indicating  apparatus  possesses  some  peculiar 
features,  as  regards  simplicity  of  details,  and  the  dispensing  with 
a  stuffing-box  for  the  commuLisating  shaft,  o,  of  the  drums.  It 
is  entirely  contained  in  the  cylindrical  brass  case,  r.  in  the  top  of 
which  a  strong  plate-glass  cover,  s,  is  screwed  in  from  the  under 
side.     A  strong  brass  plate,  T,  divides  the  case  from  the  meter, 


and  has  a  central  hole  for  the  passage  through  of  the  vertical  spin- 
dle, o.  A  worm,  or  endless  screw,  u,  upon  this  spindle,  gives 
motion  to  the  wheel,  v,  the  horizontal  spindle  of  which  has  a  worm, 
w,  cut  upon  it,  and  gearing  with  a  horizontal  wheel,  x.  Tho 
spindle  of  this  latter  wheel  carries  a  broad  pinion,  Y,  which  drives 
both  the  horizontal  spur-wheels,  z,  the  fust  of  which  has  101,  and 
the  second  100  teeth. 

The  wheel  with  101  teeth  works  loose  upon  its  spindle,  but 
carries  round  with  it  a  dial-plate,  a,  graduated  on  its  circumference 
to  100  parts.  The  lower  wheel  of  100  teeth  is  fixed  upon  tho 
same  spindle  as  the  first,  and  carries  an  index  hand,  which  works 
round  above  the  dial,  and  points  to  the  divisions  thereon ;  and  a 
fixed  hand,  J,  points  as  well  to  the  same  graduations.  The  train 
of  worm-wheels  is  so  proportioned,  that  exactly  10  gallons  of  water 
must  pass  through  the  meter,  in  order  to  move  the  dial-plate  under 
the  fixed  hand  through  one  division.  One  entire  revolution  of  the 
dial,  consequently,  indicates  the  passage  of  1,000  gallons  of  water, 
for  which  tho  moving  differential  hand  passes  through  only  a 
single  division  on  its  dial.  An  entire  revolution  of  the  latter, 
therefore,  signifies  the  passage  of  100,000  gallons.  The  reading 
of  such  a  dial  is  extremely  simple.  If  we  suppose  the  fixed  hand 
to  point  to  47,  and  the  hand  on  the  dial  to  89,  this  will  show  that 
89,470  gallons  have  passed. 

The  whole  chamber  of  the  counter  is  filled  with  purified  mineral 
naphtha,  or  other  non-corrosive  liquid,  which  communicates  with 
the  impure  liquid  passing  through  the  meter,  only  through  the 
medium  of  the  capillary  space  round  the  upright  spindle,  o,  and 
does  not  intermingle  with  ^although  both  liquids  are  under  the 
same  pressure. 

The  actual  measurements  by  this  meter  have  been  found  to* 
agree  so  perfectly  with  the  calculations,  in  which  the  frictional 
surfaces  against  the  water  are  taken  into  account,  that  llr.  Siemens 
considers  any  means  of  adjustment  to  be  unnecessary.  Much, 
however,  depends  upon  the  formation  of -perfect  screw  vanes  upon 
the  drum,  to  insure  uniform  results :  but  all  difficulty  on  this  head 
has  been  very  successfully  removed,  by  casting  the  drums  in  metal 
moulds,  using  a  peculiar  composition,  which  does  not  shrink  in 
cooling,  and  runs  very  fine. 

The  only  parts  of  this  meter  where  wear  and  tear  is  to  be  ex- 
pected, are  the  pivots  of  the  rotatory  drums,  and  these  are  made 
of  hard  steel,  and  abut  against  agate  plates  ;  'but  considering  that 
all  weight  is  taken  off  the  bearings,  and  that  the  water  simply  elides 
over  the  drum  surfaces,  these  pivots  may  reasonably  be  expected 
to  run  for  years  without  requiring  attention. 

An  important  practical  advantage  of  this  form  of  meter,  is  its 
compact  form,  and  the  facility  which  it  offers  for  adjustment  in  a 
line  of  pipes  below  street  pavement,  or  at  any  required  elevation 
or  direction.  The  internal  working  parts  are  qujte  self-containi  d, 
and  inaccessible  widiout  unsoldering  the  ends,  so  that  they  may  be 
intrusted  to  the  care  of  ordinary  workmen. 

In  addition  to  the  employment  of  the  meter  for  water-works 
purposes,  it  may  be  usefully  applied  for  registering  the  water  sup- 
plied to  steam-boilers,  in  order  to  ascertain  the  actual  evaporation 
going  on,  so  as  to  afford  a  correct  estimate  of  the  value  of  the  fuel 
on  the  one  hand,  and  the  engine  and  boiler  on  the  other. 


Til.:    1 


BB  \!'IN<;    M  \>   Hi 

PLATE  3. 

Oar  aeeoad  t'T**  plal*  is  in  a  marc  ai. 

.'.usst,  and,  s»  a  work   of  high<  r  .  a  moat 

■J|«u|»mtl  subj.-ct   for  the  a 

It  goes  further  than  Plat*  A.  in  as  lar  as,  in  addition  to  it-,  value 
t,  a  fc^  ■  nta   aome   mml    important 

features  of  symmetry  in  ita  abstract  design,  and  • 

■mlainii  al  di» 

trirance,  and  l!  -°  details.     T>. 

of  to  good  a  design  U 

When  WaU  was  laying  the  foundation  of  our  present  magniii- 
\.  ■  I   •:.. .  haai  a     ..  '-.  :.•    '-....-  I:.-  :  a:  ■  W  -ry  tuni  bj    |  - .  ■■- 

lieal  dimraltirs,  in  tin-  want  ■■: 
hit  ideas;  and  many  1 

to  remain  mere  suggestive  designs.     For  the  same 
numberless  works,  which  the  growth  of  mechanical  con- 
trivances has  turned  into  even-day  opera!]  ited  and 

>  B  aa  simple  impossibilities,  in  the  'i 
were  made  by  the  crude  process  of  wrapping  a  wire  round  a  man- 
drel, and  compressing  it  between  elastic  dies.     But  I 

•  •ur  farm  operations  have  begun  to 
feel  the  benefit*  of  machinery;  and,  as  a  1 
we  now  find  establishment/,  for  making  and  repairing  stean. 
and  other  intricate  mechanistn  This 

substitution  of  machine  tools  for  hand  labour,  whilst  it  has  intro- 
duced great  accuracy  of  workmanship 
that  cheapoess  of  1  with  the  ap| 

of  new  1  1  i  materials,  has  made  us  the  eminent  manu- 

ic  are. 

I  is  also  latterly  met  with  increased 
- 
tails,  sjm)  '.'.  ;  for  the  at 

naturally  cares  more  for  an  elegant  macliiu-  ne  than 

for  one  :  ride  far 

-     •  wees. 

:ithc  is 
1   most  ancient,  and  it 

applica- 
I  its  action.     1 

Anally  accumulated  st-parat- 
planing.  - 

-  .ially  adapted  tools.     Each 
1  r.  and  ia  reatricted  to  a  particular  • 

many  separate   I 

•  i  mechanism.  :ve  of 

•■  in  transferrin;:  and 
....  chances  of 
readjustment.      And    in    many   branches   of   manufacture 

.  advan- 
aae  of  the  several  kinds  dis- 


courages their  adoption.     We  are,  therefore,  drive: 

w-hich  ahall 
v. sting  detached  tools. 

Arts,  ha?  'ally  alluded  to  this,  in  speaV 

of  "  machine*  much  more  comprtl.-  -;mple  in  form, 

by  mea   -  in  general  will 

:.truduced  into 
;•  of  a  smaller  character  than  at  present,  in  the  same  man- 
ner as  t  -  -aw  haa  eadca 

- 
upon,  the  common  lathe  a- 

:  -ns,  arranged  by  Mr. 
"«■  combination  of  the  ordinary  cirrular-cut- 
..:.d  arrangements  of  the  lathe,  wit!, 
1'ing  machine,  or   f 
I  e  may  be  applied  to  most  of  the  «"*-*""« 
'  useful  and  ornamental  manu- 
al in  the  arrangement  of  coo- 
Thus,  in  the  case  of  the  lathe,  for  example, 
1  kinds  of  plain 
work,  but  -ranch  of  coro- 

trical  turning.     For  instance,  if  the  sliding  bar  carry- 
rkod  by  an  adjustable  crank-pin,  u 
a  slot  in  the  end  of  thi 

;he  lathe  nv. 
the  interposition  of  the  ordinary  chi  :)ie  lathe,  most 

. 
kinds  of  lathes  may  bo  executed — as  eccentric,  • 
■  'idal,  and  01! 

-  angularly,  by  the  adjustment 
ply  ne- 
cessary t"  al'<  r  tin    : 

s  a  prominent    feature   in   I 
:\idual  parts,  like  the  machi: 

-  •  that  a  lathe, 
enitirai-i:  —ess  the 

the  ordinary  plain  work 
of  the  amateur      The  engineer  ami  niechai:  -  re  these 

.  hange- 

- 
,  ams,  snails,  spirals,  and  \  1 

circular 
or  rectilinear,  and  for  pUnir  .  I  angular 

gearing  of  a 

.     lathe,  in   which    a  •     maiu    sirii . 

actuating  the  mandrel,  B,  of  the  lathe  by   means  of  a  pinion,  c, 

..r  by  a  clutch:  d,  back  gearing  for 

slow  speed,  as    usuai  screw,  with 

.  guidc- 

- -aft  for  actuating  t!  -ltd*   of 

the   sli-:  :ig;  L,  the  same  for   moving 

of  the  guide-  v  red  shaft,  in  connection  with  the  dif 


BOOK   OF   INDUSTRIAL   DESIGN. 


ferential  or  barrelling  motion,  wjiich  is  attached  to  the  vertical 
slide,  and  consists  of  a  segmental  screw-wheel,  embracing  a  mo- 
tion of  about  G0°,  gearing  with  a  tangent-serow  on  the  shaft,  L.    The 


segment  has  a  radial  slot,  in  which  an  adjustable  crank-pin  is  fixed, 
the  crank-pin  being  attached  to  the  bearings  of  the  screw  for 
moviug   the   vertical   slide,  by  means    of  a   connecting-rod — thn 


Fig.  2. 


bearings  of  the  screw,  which,  slide  in  dovetails,  and  consequently 
the  vertical  slide,  being  thus  affected  by  the  eccentricity  of  the 
crank-pin.  The  shafts,  A,  H,  and  I,  and  screws,  g  and  K,  are  con- 
nected by  a  system  of  wheels,  the  arrangement  of  which  is  clearly 
shown  in  the  end  view,  fig.  2  ;  but  G,  H,  I,  and  K,  may  be  discon- 
nected from  their  respective  wheels  at  pleasure  by  clutches  or 
frictions]  nuts,  a,  g,  h,  i,  and  l,  also  project  at  the  end  to  the 
right  hand  of  fig.  1,  so  as  to  carry 
change-wheels  when  necessary, 
and  H  and  I  have  intermittent 
ratchet-feeding  movements  at  the 
opposite  end,  similar  to  that  at  E, 
for  working  the  tangent-screw. 
All  these  are  worked  by  the  re- 
versing bar  in  connection  with 
the  screw,  K.  An  ordinary  re- 
versing movement,  M,  is  interposed 
between  the  guide  screw,  e,  and 
its  driving-wheel,  for  reversing 
the  motion  in  sliding  and  screw- 
cutting.  When  the  lathe  is  used 
for  surfacing,  this  reversing  motion 
is  better  applied  on  the  driving-shaft,  A.  Hand  adjustments,  not 
shown  in  the  figure,  are  applied  to  the  boxes  of  the  guide-screw,  g, 
and  of  the  screws  of  the  vertical  and  transverse  slides  of  the  slide- 
rest.  A  composite  lathe,  thus  geared,  may  be  applied  to  all  the 
ordinary  descriptions  of  work.  For  sliding,  boring,  and  screw- 
cutting,  the  mandrel  is  worked  by  the  pinion,  c,  whilst  change- 
wheels  connect  a  with  a.  The  height  of  the  tool  for  turning  is 
conveniently  adjusted  by  the  vertical  slide  of  the  slide-rest.     Sup- 


pose it  is  desired  to  stop  the  lathe  at  any  particular  point  when 
the  attendant  is  absent,  the  screw,  K,  is  put  in  gear  by  its  clutch, 
and  by  means  of  a  detent  stop-movement,  it  stops  the  lathe  at 
the  precise  point,  by  throwing  the  belt  off  the  fast  pulley  on  the 
end  of  A,  which  travels  with  considerable  rapidity.  If  it  be 
required  to  turn  a  long  cone  of  greater  taper  than  can  conve- 
niently be  done  by  traversing  the  following  head-stock,  the  cut- 
ting-tool is  set  over  the  work  by  raising  the  vertical  slide  by  its 
hand  adjustment,  whilst  G  and  i  are  also  connected  by  change- 
wheels,  so  that  the  slide  rises  or  falls  with  the  cut.  If  a  con- 
necting-rod is  to  be  barrelled,  the  crank-pin  of  the  differential 
apparatus  is  adjusted  for  eccentricity  to  suit  the  rise  of  the  sweep, 
and  l  is  connected  with  G  by  the  change-wheels,  to  spread  the  are 
over  the  required  length.  The  barrelling  may  be  used  in  conjunc- 
tion with  the  taper  adjustments,  as  will  be  evident  to  the  practical 
mechanic.  The  same  parts  apply  equally  to  rectilinear  cutting, 
whether  parallel  or  taper,  in  all  directions  of  the  cube,  and  for 
barrelling  in  a  vertical  plane,  the  pinion,  c,  being  disconnected 
with  the  mandrel,  and  the  feed  being  applied  by  the  intermittent 
ratchet  motions.  For  cutting  the  hollows  of  connecting-rods, 
&c,  an  intermittent  revolving  motion  is  given  to  the  tool  by  a 
tangent-screw  movement  as  usual,  but,  in  addition,  applying  to 
cranks  and  levers  held  on  the  face-chuck ;  or,  instead  of  the  latter 
movement,  the  work  may  be  set  eccentrically,  the  hollows  being 
then  worked  by  the  tangenkserew  movement  in  connection  with 
the  mandrel. 

Edge-cams,  snails,  volutes,  of  spiral  curvature,  with  any  num- 
ber of  rises,  or  compounds  of  circular  and  spiral  arcs,  of  which 
fig.  3  gives  examples,  may  be  accurately  shaped  or  planed  on  the 
edges,  by  connecting  the  tangent-screw  with  the  transverse  slide 


I 

L'..    ntrdcC-frxl  moirmenU  of  r.  sod  I  sre  put  in  p-ar,  i  being 


ninn,  *, 
.  whilst  I  an.l  ! 

.  una  and  othi  i 
may  be  shaped  l.y  va- 

.  it  aifl  diagonal  work  in  any  position  mny  also  br  I 

-        the  satue  set  of 

such  as  B  a  c.  • 

n  c,  or  sine  of  the  angle,  whilst  the 


other  ande  traverses  •  r.pj.lv  Ada  practically, 


tii»n  in  the  rvmainin;;   direeaoa  >•(   tlie   cube.        I 

-  introduced  into  tlic  pair  of  change- 
In  many  ca.v>«  a  crank  Fit  «. 

in  addition  to  I 

• 
nunt,    t 

whOe  d 

■  i  to   ailju-t   tlie 

I 
« 1  i  — . -  i<  than  ilriwn  by  a 
bc\il  pinion  on  I 
A,    the 

ttaehed   to  ona 

of  tli<'  bearingi  of  the 

raw,    which    U 

-imilarly 
to  tlie  barrelling 
tin  nt. 

•':•■   lathe,  or  shaping  machine,  con- 

atmctad   on  the  model   of  tha  ordinary  planing  maebJi 

irately    linisliin^'    tlic 
ing  tha  framingi  of  marina 
hi,.!  other  •  I 

appUaahla  to  n  rariety  of  other  wi 
it  eon  tha  lathe  whh 

i  rdinary    <lrii: 

: 

^•■rk  i^  plaa 

upright  itawdaHt i  a  a,  a*  in  tha  ordinary 
planing  machim  .  whflal  ■  verticaJ  i 
may  be  given  to  tin 
•  ■.■k,  earrying  lha  lathe  mandrel, 
bj  two  eonnecting  i  ■■•  'I  by 

crank  ■  the  bad,  and  ba 

If  m  .  i  .Is  are 

adjustable  for  length  by  moana  ofacrose 
■haft,  •  w-wheel  and 

1,  ;     D  i"  the    ' 

motion,  as  ii- 

gulate  tha  eccentricity  of  the  tool  daring 

turiiii  h  mny 

be  automatically   fed,  when   requisite,  by 

an  eooi  otrio,  do)  shown  in  the  I  \ 

-   Hon,  and 

another  ai  lha  baeh  of  the  ande,  s,  wUofa 
it  aetnataa,  adjnata  lha  mandrel  hi  a  »ar« 
Heal   plane.    By  Um  dhnjtmal   p 
wa  deasribed,  the  ootagonaJ 

for    plmmniT-l.liH'k   bnuwes,    and 
ilar  work,  may  be  aSeOUted  with  ptl 

no  ..t   In  .1.    Tha  baoVchnek 

BO   tli"    side,  as  used   for  holding    p!uiiiiiirr-lilo.-k- 


BOOK  OF   INDUSTRIAL  DESIGN. 


their  soles  are  pla  led.  A  second  chuck  (dotted)  maybe  super- 
posed for  fixing  work  vertically;  and  a  slide  may  be  added  to  draw 
up  the  work,  which  may  then  project  between  the  bearers  of  the 

l>ed.  For  long  works,  a  bed-chuck  is  used  at  each  end  Levers, 
also,  may  bo  passed  between  the  bed,  by  means  of  a  diametric  slide 
on  the  face-chuck,  when  requisite. 

We  now  eome  to  Plate  3  itself  in  detail.  That  plate  repre- 
sents a  side  elevation  of  a  composite  slotting  and  shaping  ma- 
chine, with  self-acting  gearing1,  as  adapted  for  the  entire  finishing 
of  large  cranks,  levers,  wheels,  and  other  work,  ordinarily  depend- 
ent upon  the  efforts  of  several  tools.  The  main  frame  consists 
of  a  lasge  and  elegant  column,  with  an  open  rectangular  base,  and 
bottom  flange  for  bolting  down  to  the  masonry.  The  upper  por- 
tion has  east  upon  it,  on  one  side,  a  pilaster  bracket  piece,  with 
two  horizontal  projecting  arms,  to  carry  the  vertical  cutting  slide, 
a  ;  and  on  the  other,  a  pillar  bracket  to  support  one  end  of  the 
main  crank  disc  shaft;  on  the  front  side  of  the  rectangular  base 
i-  I'.  Ited  a  double-armed  bracket,  to  carry  the  vertical  spindle  of 
the  cutting  face-chuck,  like  the  mandril  and  face-plate  of  a  large 
lathe,  as  set  on  end.  The  cutting  slide,  A,  like  that  of  a  common 
slotting  machine,  is  fitted  to  traverse  in  dovetail  faces  on  the 
overhead  bracket  arms,  being  actuated  by  the  revolution  of  the 
pin  iu  the  disc,  b.  At  c  are  two  pairs  of  bevil  pinions,  connected 
to  work  simultaneously  by  an  intermediate  vertical  shaft,  D,  the 
two  vertical  pinions  being  each  on  the  projecting  end  of  a  hori- 
zontal screw  spindle,  governing  the  traverse  motions  of  a  pair  of 
Horizontal  dovetailed  slides,  on  which  the  vertical  slide  faces  of 
the  slotting  bar,  a,  are  carried.  This  is  for  adjusting  the  eccen- 
tricity of  the  tool  in  turning.  Viewed  from  the  front,  the  fram- 
ing of  these  slides  has  the  form,  I,  of  which  the  vertical  portion 
and  the  two  arms  to  the  left  are  covered  by  the  moving  details, 
the  latter  being  completely  thrust  in  when  the  cutting  tool  of  the 
slide,  A,  exactly  coincides  with  the  centre  of  the  revoking  work 
en  the  face-chuck,  as  also  with  the  crank  disc,  b.  At  E  is  an- 
other shaft  for  giving  a  continuous  feeding  motion  to  the  trans- 
verse slides,  by  the  intervention  of  a  worm  and  tangent-screw,  or 
worm-wheel.  This  corresponds  to  the  traverse  or  surfacing 
movement  in  the  lathe.  A  hand-wheel,  F,  is  fitted  on  the  pro- 
longed end  of  the  shaft,  D,  for  manual  adjustment  when  the  worm- 
wheel  gear  is  disconnected  by  slackening  the  screw,  g,  the  bear- 
ing, H,  at  the  other  end  of  the  spindle  being  constructed  with  a 
joint  to  allow  of  this  disengagement.  Another  shaft,  i,  carries  a 
spur  pinion  to  actuate  the  rack,  j,  on  the  cutting  slide,  this 
pinion  being  capable  of  traversing  on  the  shaft  by  means  of  a 
groove  and  feather,  along  with  the  slides  of  the  cutting  bar.  In 
this  way  a  continuous  vertical  feed  motion,  for  turning  or  boring, 
is  secured,  the  shaft,  I,  being  connected  with  the  shaft,  k,  by  a 
worm  and  wheel ;  the  hand-wheel,  l,  on  the  bottom  end  of  a  ver- 
tical shaft,  connected  at  its  upper  end  to  the  shaft,  K,  by  a  pair  of 
bevil  pinions,  is  the  hand  adjustment.  This  motion  serves  also 
to  adjust  the  cutting  bar,  previous  to  tightening  the  nut  on  tho 
stud  bolt  in  front,  for  the  reciprocating  action.  During  the 
working  of  the  reciprocating  cutter  slide,  however,  this  adjusting 
gear  is  disengaged,  and  is  kept  disengaged  by  an  eccentric  and 
slide  actuated  by  the  hand-wheel,  n,  which  moves  the  entire 
adjustment  in   one  mass.     At   the   back  of  the  cutter  slide,   near 


the  upper  end,  is  a  nut,  o,  whereby  the  crank  disc  connecting-rod 
may  In-  detached  when  wide  lateral  ranges  of  the  slide  are  wanted 
in  turning.  The  general  details  of  the  driving  gear  for  the  turn- 
ing and  planing  actions,  are  fully  delineated  in  the  plate  :  but  it 
may  be  explained,  that  at  V  is  a  hand-lever,  working  over  a  semi- 
circular arc,  suitably  notched  and  contrived  to  snift  the  bearing, 
Q,  of  the  horizontal  shaft,  B,  by  an  eccentric,  so  as  to  throw 
either  of  the  opposed  or  antagonistic  bevil  wheels  on  this  shaft  into 
gear  with  its  corresponding  bevil  wheel.  This  movement  enables 
the  workman  to  connect  either  the  circular  action  of  tin-  face- 
chuck,  through  the  large  bevil  wheel  beneath  it,  or  the  rectilinear 
action  of  the  cutting  slide,  by  means  of  the  vertical  shaft  passing 
up  the  centre  of  the  maiu  column,  and  geared  to  the  horizontal 
crank  disc  shaft  above,  by  a  bevil  wheel  and  pinion,  or,  by  selling 
this  adjustment  at  an  intermediate  position,  both  may  be  disen- 
gaged. At  s  is  a  foot-break  lever  to  stop  the  revolution  of  the 
work  when  heavy  masses  are  under  operation,  a  friction  strap 
from  this  lever  being  passed  over  a  pulley  on  the  shaft,  R,  for  ibis 
purpose. 

At  T  is  a  cone  pulley,  working  in  connection  with  the  cone  pul- 
leys on  the  two  upper  or  continuous  feeding  shafts,  for  the  circular 
cutting  action,  the  respective  pulleys  being  set  to  coincide  verti- 
cally when  connected.     The  face-chuck  can  be  fixed  during  the 
reciprocating  action  of  the  cutting  slide,  by  the  clamp,  u.     This 
clamping  movement  consists  of  a  worm,  with  a  square  spindle  for 
shipping  on  a  handle,  driving  a  worm-wheel  on  the  end  of  a  spin- 
dle, connected   interiorly   with  a  segmental   wedge,  the    sides  of 
which  are  portions  id' a  right  and  left  screw-thread   respectively. 
The  upper  part  of  this  segmental  piece  is  flattened,  to  permit  the 
free  revolution  of  the  face-chuck  when  driven  by  th 
ing,  as  indicated   by   the   large  worm-wheel,  in   gear   with 
fast  on  the  spindle  of  the  main  front  hand-wheel.     Near  it 
of  the  tool  is  a  hand-wheel,  v,  for  the  angular  adjustment 
mandril  frame  or  headstock  for  taper  work.     For  ibis  purpose  the 
headstock  is  attached  to  the  main   frame  by  a  central   tenon  and 
circular  dovetails,  which  afford  a  support  during  the  slackening  of 
the  holding  bolts. 

An  eccentric  chuck,  having  two  slides  at  right  angles  to  each 
other,  ami  an  upper  worm-wheel  adjustment,  is  titled  on  the  facc- 
chuek  mandril.  The  lower  slide,  for  giving  the  intermittent  feed 
in  shaping  the  rectilinear  sides,  w,  of  a  crank,  has  a  double-acting 
ratchet-wheel,  temporarily  connected  by  a  rod  with  the  correspond- 
ing feeding  disc  of  the  large  worm-wheel  on  the  face  chuck,  when 
the  latter  is  fixed  at  u.  The  intermittent  feed  is  primarily  derived 
from  the  edge-groove  cam  on  the  crank  disc,  B.  This  groove  works 
the  upper  stud-pin  of  a  bell-crank  lever,  set  on  a  stud  centre  in  tiie 
side  <d'  the  main  frame,  and  from  the  lower  horizontal  arm  of  this 
lever  a  rod  descends  to  the  worm-wheel  mechanism  of  tie  i.  >  - 
chuck. 

The  upper  side  of  the  eccentric  chuck  is  limited  to  the  ac- 
tual adjustment  of  the  work,  and,  by  means  of  the  two  slides 
conjointly,  adjustments  may  be  made  for  shaping  the  bosses  of 
the  cranks,  as  well  as  the  hollows  at  x.  The  obliquity  of 
the  straight  sides,  w,  of  the  crank  is  adjusted  by  the  upper 
screw-wheel,  which  need  only  bo  of  a  diameter  equal  to  tho 
length  of  the  crank  ;  or,  instead  of  this  plan,  the  sides,   w,  may 


U  worked  .-at  ilnVrrolialli   by  <k' 

la  ralti n .•  . .«!  a  crank  on  : I 
fared.     TV  buam  an 

bat  fitted  .-  :■   v  ■   leal   of  bj  moani  of  i!.-    :  in      ;  '•■■  I      A/li  r 
rk   ha*   U«-a  a»Iju*tt-«!    . 
ii  ilaiii|iiil  ilnaii  mil  ■  In  '" 
I-./  x  ,t..,.,c  b  the  i-lim  k,  >•  lli-  n  )ci-~^l  :!,r.ujli  the  boro  ■•f  each 
bow,  and  thr  external  etamr~  I  taming 

»r»l  .lii|»n„'  protussss  an-  gone  through.    The  »Tk  requires  no 
further 

b-»\»  work  tli_m  ibr  lal 

' 

■  •:i  in  a 
plait*,  a»  oa  a  latin-,  entail*  w  ;  liability 

able  by 
■ 

nee,  but 

i 

a  In.  I,  cannot  be  »<j  turned  in 

il  column,  with 

it.     Tin-  crank 
-    ' 
-.   n-turn  ;  ami   I  In  (rant  of  thfl 

mi  nt  to 
I  01 

r  when 

daaeenda  into  a  pit,  so  as  to  bring  the  d  derably 

.  in-ular 
I  1- 1*1  down  solid  i*.r 

.'  worm  "r  t:in- 

•  with  n 

mail  behind,  an<l  Iht  required  an-  is 

nk  |'iti  rnrlin-  I 
■ 

nil. 

but  the 

•  at  right  anr- 
t"  a[.p'.  and  tuning, 

I 

■  hack,  ud  ■  ■ 

!•.  th*  fa.-.   • 
either  a  worm  at  tin-  fr.mt  tn.l  ma.  turn  the 


: 

ed,  as  i. 

■ 
Ii  ft  thread  may  lw  pul 

for  tin. 

with  tli- 

v. 

plank, 


EXPRESS  LOCOMOTIVE  ENGINE 

The  three  pUl  .  far  tlio 

kiml    in  r    •  \ 

di  pth  of  lining, 
where  every  Individaal 

f  the  i  i 

■ 

of  the  boiler  at  the  steam  dome,  aho  ■  •  •!  Iha 

Innermost  expanded  p 
section  is  taken  at  a  point  al 
neck  ••!  I  i 

dbtthxl  half  section*,  one  through  the  mo 

•  r    llir..il_'!i    l1.. 

ide  with  iosidi 
'  tnd  *i\  wheel*;  the  driving-wheel 

diameter,  and  arranged  In  the  mannoi 
Tin-  < 

n|i  with  pistons  mado  of  w 
be  made  by  lir.  GoodfeUou   •  •!  Manchester.    The  eylu> 
,1,  r- 1->  be  of  the  hardeal  an 

an. I  Inn-  when  fitted      The 

cylinder 

p.irH  a- 

Ibr  the  i 

The  B  n  ''"■  eyllnder, 

and  four  fcet  three  and  ■  quarter  Inches  i  sternal  d 

llv  i-ir.-nlar  .-.  I 

la, '..  I.--  of  the  beat  Lowmoi 
qoality,  with  the  nal 

]     .     rU.  1-  !■■  I- 

sn.l  to  be  one  and  three  quarter  Inehi  -  apart  from  i 
of  rivet.    The  plat**  for  the  cyllndi 

f  an  inch  in  tlii.ktn  ■■■r  tl titer  — 1 1«  - 1 1  of 

la  I f  Lowmooror  Bowing  Iron,  or  ol  equal 

•  f  an  Inch  in  i'  as  of  lh« 

!  B 


BOOK  OF  INDUSTRIAL  DESIGN. 


£..,11:11  quality;  to  be  three-fourths  of  an  inch  thick.  The  plates 
of  tho  smoke-boxes  and  smoke-box  door  to  be  of  the  best  Staf- 
fordshire iron,  live-sixteenths  of  an  inch  in  thickness.  The  chim- 
neys tu  be  made  also  of  Staffordshire  iron,  one  quarter  of  an  inch 
in  thickness  ;  and  the  whole  of  the  parts  of  the  boilers  and  smoke- 
boxes  to  be  made  and  fitted  up  in  the  manner  shown  in  the  draw- 
ings, which  will  be  supplied. 

The  Fire-boxes  to  be  mado  as  shown  in  drawing,  and  introduced 
as  shown  in  tho  cylinder  part  of  tho  boiler,  four  feet  nine  inches; 
to  be  made  of  the  best  copper  plate,  free  from  all  delects  when 
worked.  The  tube-plate  to  be  three-fourths  of  an  inch  in  thickness 
where  the  tubes  are  fixed.  The  sides  and  end  plates  to  be  three- 
eighths  of  an  inch  thick,  and  the  roof-plates  to  be  seven-sixteenths 
of  an  inch  thick.  The  bottom  plates  to  be  one-half  inch  thick.  Tho 
boxes  to  be  made  with  a  middle  partition  in  them  ;  the  plates  of 
these  partitions  to  be  of  copper,  made  three-eighths  of  an  inch  in 
thickness,  and  formed  as  shown  in  drawing. 

The  following  are  the  leading  inside  dimensions  of  tho  fire-box  : 
— Length  on  Sre-bar  to  be  five  feet  ten  inches  and  one  quarter. 
The  length  at  roof  to  be  ten  feet  six  inches.  Depth  above  fire- 
bars at  front  plate,  six  feet  fivo  inches.  Depth  at  door-plate,  six 
feet  ten  inches.  Width  on  fire-bar,  four  feet.  Length  in  cylinder 
of  boiler,  four  feet  nine  inches.  Height  at  narrowest  part,  two  feet 
three  inches.  Height  at  tube-plate,  three  feet.  Width  at  tube- 
plate,  three  feet  nine  inches. 

The  top  of  tho  box  to  be  supported  by  twenty-five  wrought- 
iron  bearers,  twenty  of  which  to  be  five  inches  deep  by  one  inch 
thick,  and  the  five  nearest  tube-plate  five  inches  deep  by  one  and 
a  half  inches  thick.  These  bearers  to  res!  at  their  ends  on  the 
side  plates  of  the  fire-box  ;  and  to  be  screwed  to  the  top  plate  by 
bolts  one  inch  diameter,  placed  four  and  a  half  inches  from  centre 
to  centre,  screwed  into  the  top  plate.  The  screw  to  be  of  fine 
thread,  next  head  of  bolt,  to  be  one  inch  and  an  eighth  dia- 
meter ;  the  head  of  tho  bolt  to  be  inside  tho  fire-box,  and  a  nut 
on  the  end  of  the  bolts  on  the  top  of  the  bearers,  with  one  inch 
screw. 

The  Fire-box  to  be  stayed  to  the  boiler  by  copper  bolts,  seven- 
eighths  of  an  inch  diameter,  screwed  into  the  plates  with  a  fine- 
threaded  screw,  having  both  ends  riveted  carefully,  and  placed  four 
inches  apart  from  centre  to  centre.  This  also  applies  to  the  mid 
partition. 

The  end  plates  above  the  fire-box  to  be  stayed  to  the  smoke-box 
tube-plate,  by  connecting  them  together  by  two  stay  bolts,  each  one 
inch  and  a  quarter  diameter. 

The  Tubes  to  be  of  brass,  and  made  the  very  best  quality,  by 
the  manufacturer  who  supplies  the  company  at  present ;  or  of 
other  equal  quality,  and  to  the  approval  of  the  company's  en- 
gineer. There  will  be  three  hundred  and  three  tubes  in  each 
engine ;  the  size,  one  and  three  quarter  inches  outside  diameter, 
to  section  furnished;  and  the  thickness  of  metal  to  be  No.  12 
wire-gauge  at  tire-box  end,  and  No.  14  wire  gauge  at  smoke-box 
end. 

The  Wheels  are  to  bo  mado  entirely  of  the  best  scrap  wrought- 
iron,  and  of  tho  very  best  workmanship.  The  driving-wheel, 
without  the  tyre,  to  bo  seven  feet  one  and  a  half  inches  diameter. 
The  tyres  to  be  of  the  best  Lowmoor,  Bowling,  or  of  equal 


quality  ;  to  be  finished  five  and  a  quarter  inches  wide,  and  two  and 
a  quarter  inches  thick  on  the  tread.  The  sizes  of  the  wheel  in  all 
its  parts  will  be  furnished  by  tho  company's  locomotive  engineer  at 
Wolverton. 

Tho  Crank  Axles  to  be  mado  of  the  very  best  iron  from  the  Low- 
moor,  Bowling,  or  the  Haigh  foundry  forges,  or  of  other  equal 
quality,  complete  and  perfect  to  the  sizes  given  when  finished.  A 
full-size  drawing  of  the  crank-axlo  in  its  parts  will  be  snpplied. 
The  outside  bearings  to  bo  seven  inches  diameter,  and  ten  inches 
in  length.  The  inside  bearings  seven  inches  diameter,  and  four  and 
a  quarter  inches  in  length.  The  crank  boarings  to  be  seven  inches 
diameter,  and  four  inches  in  length. 

The  Straight  Axles  to  be  tubular,  as  shown  in  the  drawing,  of 
best  quality  of  iron,  seven  and  a  quarter  inches  external  diameter, 
and  one  and  a  half  inch  thick  of  metal.  Tho  bearings  of  the  lead- 
ing and  trailing  axles  to  be  the  same  size  as  the  crank  ;  viz.,  seven 
inches  diameter  by  ten  indies  long. 

Tho  Axle  Boxes  and  brass  bearings  to  be  mado  according  to  the 
drawing  which  will  be  supplied. 

The  Springs,  links,  and  attachments  to  the  axle-boxes,  to  be 
supplied  by  the  company,  and  applied  according  to  the  instructions 
of  their  engineer  at  Wolverton. 

The  Pumps  to  be  made  of  tough  brass  to  the  drawing  furnished. 
The  clacks  and  boxes  to  be  accurately  finished  and  fitted.  The 
pump-rams  to  be  made  of  strong  tough  brass,  with  wrought-iron 
cross-heads,  as  per  drawing. 

The  Steam  Pipes,  blast  and  feed  pipes,  to  be  made  of  the  best, 
copper,  three-sixteenths  of  an  inch  thick,  with  copper  flanges,  as  per 
drawings  to  be  supplied. 

Regulator  to  be  made  of  brass,  on  the  equilibrium  principle,  ad 
per  drawing. 

The  Eccentric  Straps  to  be  made  of  the  best  wrought-iron,  lined 
with  gun  metal  of  die  best  quality,  according  to  drawing,  accurately 
fitted,  and  to  have  all  the  oil  siphons  forged  on. 

The  Slide  Valves  to  be  made  of  gun  metal,  and  to  have  an  out- 
side lap  of  one  and  a  quarter  inch.  They  are  to  have  an  oil 
or  grease  cup  attached  on  each  side  of  the  smoke-box.  to  lubricate 
them. 

The  Connecting-rods  to  be  made  of  the  very  best  quality  of 
wrought-iron,  fitted  accurately.  The  straps  to  be  made  as  per 
drawing,  and  the  oil  siphons  to  be  forged  on  them. 

The  Expansion  Gear  to  bo  made  as  per  drawing,  all  the  work- 
ing and  Wearing  joints  and  surfaces  to  be  steeled  and  hardened,  or 
case-hardened.  The  distance  from  the  centres  of  the  leading  wheel 
axle  to  the  centres  of  the  middle  axle,  to  be  exactly  eight  feet  four 
inches,  and  from  the  centre  of  the  middle  to  the  centre  of  the  trail- 
ing axle,  eight  feet  six  inches. 

These  Engines  are  to  be  manufactured  of  the  very  best  mate 
rials  and  workmanship  throughout,  and  supplied  in  every  respect 
with  water-gauges,  steam-taps  for  heating  water  in  tender,  whistle 
blow-off  cocks,  cylinder-cocks,  pet-cocks,  reversing  and  expansion 
gear  worked  from  tho  foot-plate ;  screw  draw-bars  (proper  and 
in  duplicate),  ash-pan,  damper,  sand-boxes,  a  full  set  of  tools,  lamp- 
in  ms,  &c 

Detail  drawings  of  all  the  parts  will  be  supplied  by  the  company's 
engineer  at  Wolverton,  previous  to  manufacture. 


TV  Svns   I  imber,  and  to  ban- 

i  -  a:.. I  ■  half  inrhea  diauivlrr, 

;lic  end 

oft!..  .  Ii  aquare  inch 

of  I]..     I 

•  aj»  of  the  apring  balance  to  bo  gm  .  ■   hun- 

dred ar. : 

.',  ao  aa 
to   be  iron  tu  iruo   »1«  :i   the  joint   U  iili.Ii-  ;    and   tin- 
be  pbmd  not  mora  loan  three  incboe  apar.  I 

I 

vtut*  made  in  two  parta,  with  a  drop  apparatus, 

■ 

robbed  down 

.   1    itll|HT- 

!  to  re- 

I  i  'oDDcll, 

r  throughout; 
t,  ahaJl  at 

■ 

b)    .Mr. 

!•  in  (he  boat 

•liii-k. 

of  the 
quality, 

• 
and  .1 

'.'iil,  will 

nr,  aa  por  drawing,  ofqoallt] 

by  the 

<•  irlng,  and 


Tbe  TrrUc- 
•ech  end;  In  i- 

: 

•  joint  •' 


\v<M>.i'i..\\i\<;  m  miiim:. 


(he  itadnl  tn 
- :  and  wbilal  il 

■ 

i.uliim-  is  il,,-  prodoetion  rail  At 

W  Foundry,    Jol 

i  iplete  longitudinal  elevation  of  tin-  im| 

machine,  aa  iii  working  order,  with  a  board  in  the 
through  it  to  I-  of  the 

machine.      Tin-    i-nlir.  ;   ii|«.n  tin-   lot 

vertical   ride  ttmHiH*i  a,  i-.-i»t  in 
down  to 

. 

Brat  motion  d 

on  to  tin-  whole  of  thi  I 

.  ning  in  bearii 

;  alley,  i,  from  which  ■ 
dl  pulley,  k,  on 
.  planing  euttor,  i..  i 

liii-  apindle  ol 
uatahle  end-bi 
of  ili.  i-  ■•  boltod  il-i"  n 

i 

which  i-ni  tin 

■ 
tudinal  centre  of  the  machine,  by  tin 

■  I.-  bud-wheel,  v,  « b 
other  ipindle,  which  it  only  tc 

,1.  «,  on  tin  - 

: 

Mil       tl|l« 


BOOK  OF  INDUSTRIAL   D] 


anil  thna  indicates  the  exact  "set"  of  the  cutters  for  the  particular 
breadth  of  timber  under  treatment 

As  the  dual  is  passed  into  the  machine  to  be  plane. 1,  it  is  first 
of  all  entered  beneath  the  nipping  feed  cams,  a,  which  carry  it  con- 
tinuously forward  to  the  out.  Each  nipping  arrangement  consists 
of  a  horizontal  traversing  plate  of  metal,  b,  tongued  at  its  opposite 
ends,  tu  slide  freely,  but  accurately,  in  corresponding  grooves  in 
the  top  plates,  c,  of  the  standards;  and  upon  these  plates,  c,  are 
attached  a  pair  of  vertical  parallel  standards,  J.  connected  at 
their  upper  ends  by  a  light  cross  bar,  e,  which  answers  as  well  for 
the  bearings  of  the  overhead  cross-adjusting  spindle,  /,  for  the 
'•set"  of  the  nippers.  Each  standard,  d,  is  slotted  down  its 
centre,  to  receive  and  guide  the  traversing  nut-bearings,  g,  of  the 
cross  cam-spindle,  h,  a  screw-spindle,  i,  being  passed  down  from 
above,  and  through  the  nuts,  g,  so  as  to  enable  the  cam-spindles, 
h,  to  be  set  up  or  down  by  the  screw  action.  This  screw  action 
is  worked,  when  necessary,  by  handles  shipped  on  to  the  end  of 
the  cross-spindle,/,  by  the  workman,  who  thus  works  the  screws 
simultaneously  through  the  two  pairs  of  small  bevil-wheels,  /. 
Each  cam-spindle,  h,  has  an  eccentric  cam,  a,  loosely  hung  upon 
it  by  an  eye,  the  cam-eye  being  entered  upon  the  spindle  up 
against  an  adjustable  collar,  A',  on  the  latter;  and  the  cam-spindle, 
h,  is  set  fast  in  the  standard  slots  by  the  outside  adjusting  nut,  I. 
Tims  arranged,  the  nipper  forms  a  complete  traversing  frame, 
capable  of  free  horizontal  movement  along  its  guide  grooves. 
Beneath  the  level  of  its  traverse  support,  two  projecting  eye- 
pieces, m,  are  cast  on  the  plate,  b,  each  eye  carrying  a  joint-stud, 
n,  whence  short  links,  o,  pass  to  corresponding  eyes,  p,  on  the 
upper  ends  of  the  two  sides  of  the  vibrating  lever  frame-piece,  q. 
Each  frame  is  carried  on  a  stud  centro,  r,  in  the  framing,  and  each 
has  a  bottom  joint-eye,  s,  for  connection  by  a  link-rod,  t,  to  the 
actuating  cam-feed  mechanism  at  the  front  or  entering  end  of  the 
machine.  Each  frame  has  also  a  heavily-weighted  bent  lever,  «, 
attached  to  its  bottom  cross  bar,  and  contrived  so  as  to  tend  to  draw 
the  tiame  continually  backward  in  the  opposite  direction  to  the 
traverse  of  the  wood. 

The  primary  movement  is  given  to  the  entire  series  of  these 
nipping  feeders — of  which  there  are  six  altogether,  three  being  at 
each  end  of  the  machine — by  a  toothed  pinion,  r,  on  the  first 
motion  shaft.  This  pinion  gears  with  a  large  toothed  wheel,  w, 
set  on  a  cross  shaft,  a\  and  carrying  a  second  pinion,  y,  in  gear 
with  a  second  spur-wheel,  z,  fast  on  the  actuating  cam-shaft,  4. 
On  this  shaft  are  keyed  the  three  separate  cams,  or  differential 
eccentric  pieces,  1,  2,  3.  Opposite  to,  and  over  the  periphery  of 
each  cam,  is  set  an  antifriction  pulley,  5,  carried  on  the  horizon- 
tal arm  of  a  bell-crank  lever,  6,  the  three  bell-cranks  being  carried 
loosely  on  a  stud  shaft,  7.  The  longer  vertical  arms  of  these 
bell-cranks  are  connected  by  eyes,  8,  at  their  lower  ends  to  the 
respective  rods,  t,  which  are  severally  linked,  as  already  de- 
scribed, by  end  and  intermediate  eyes,  to  the  bottom  of  each  of 
the  nipping  frames.  The  three  cams  are  so  set  at  starting,  that 
they  aha]]  each  act  at  different  periods  of  the  revolution  of  their 
carrying  shaft,  in  such  manner  that  a  uniform  feed  action  may  bo 
given  to  the  board  passing  through  the  machine.  In  other  terms, 
they  are  set  at  equal  distances  asunder  in  the  direction  of  revolu- 
tion of  their  shaft,  each  cam  being  linked  to  and  made  to  actuate 


two  nippers.  Thus,  the  corresponding  nippers  of  each  pair  nave 
always  the  same  relative  position,  as  marked  1.  2,  and  3.  Then, 
as  the  planing  goes  on,  and  the  cams  revolve,  each  pair  of  nippers 
is  made  to  traverse  forward — -say  in  the  direction  of  the  arrows  at 
1 — by  the  upward  revolving  action  of  the  corresponding  cam.  This 
forward  traverse  is  the  positive  feed  action  ;  for  the  moment  the 
nipping  frame  moves  in  this  direction,  the  prominent  eccentric 
portions  of  the  cams,  a  1,  are  thereby  carried  down,  or  jammed 
hard  upon  the  upper  surface  of  the  timber,  squeezing  it  firm  down 
upon  the  bottom  plates,  h,  so  that  the  timber  is  carried  forward  to 
the  cut,  as  if  it  were  permanently  attached  to  the  nipping  I',  ed- 
framo.  Whilst  this  positive  feed  is  being  given  to  the  wood,  the 
two  pairs,  2,  of  the  nippers  are  being  brought  bach  by  the  action 
of  their  weighted  levers,  as  their  corresponding  cam  is  descending 
in  its  revolution  ;  these  two  nippers  are  consequently  slipping  over 
the  wood,  for,  on  the  instant  of  the  return  movement  towards  t In- 
entering  end  of  the  machine,  the  prominences  of  the  nipping  cams 
are  drawn  out  of  nipping  contact,  and  the  frames  go  back  without 
interfering  with  the  feed  traverse  of  the  wood  in  the  forward  direc- 
tion. As  delineated  in  the  plate,  the  third  pair  of  Dippers  are  -.till 
in  forward  gear,  and  acting,  by  reason  of  the  position  of  their  actu- 
ating cams,  to  carry  forward  the  wood  in  concert  with  the  nippers, 
1.  By  this  means,  as  each  cam  comes  round,  it  gives  its  forward 
feed  and  back  traverse  in  regular  uniform  succession,  each  succeed- 
ing nipper  gradually  relieving  the  last  in  feeding  action.  And 
although  two  nippers  always  thus  tend  to  come  into  action  at  the 
same  time,  derangement  cannot  ensue  from  this  cause,  inasmuch 
as  the  quickest  forward  feeding  nippers  at  any  given  moment  carry 
forward  the  wood  free  of  the  other  nippers,  which  give  way  in 
their  nipping  action  to  the  higher  rate  of  motion,  by  reason  of  the 
consequent  slip  or  disengagement  of  the  nipping  cam.  In  this 
way  the  feed  is  constantly  uniform,  as  although  it  is  furnished  by 
three  separate  actions,  yet  each  only  comes  into  actual  feeding  play 
at  the  moment  that  it  is  required  to  keep  up  the  regularity  of 
movement. 

As  the  board  is  thus  carried  forward,  it  comes  first  above  uio 
three  finishing  planes  in  the  frame,  9,  over  which  it  is  held  down 
by  the  three  rollers,  10,  which  run  in  adjustable  bearings  held 
down  by  the  helical  springs,  11,  adjustable  to  any  desired  tcn- 
sional  pressure  by  the  nuts,  12,  on  their  screwed  spindles,  13. 
carried  in  the  stationary  frames,  14.  After  passing  these  press- 
ors, the  emerging  end  of  the  wood,  as  planed  and  finished  on  its 
under  surface,  proceeds  beneath  the  duplex  pressing  pulleys,  15. 
set  on  a  stud  centre  on  theyfree  end  of  a  lever  arm,  Hi,  fast  to  the 
horizontal  shaft,  17,  carried  in  end  bearings,  18,  in  the  end  frame, 
and  held  down  by  the  lever  and  weight,  19.  Thence  it  enters 
beneath  the  pair  of  horizontal  pressing  rollers,  20,  similarly  held 
down  by  adjustable  helices,  21  ;  and  it  is  between  these  two  rollers 
that  the  planing  of  the  upper  surface  takes  place.  At  the 
moment,  however,  of  its  passage  beneath  the  duplex  pulley.  15,  it 
is  first  acted  upon  by  the  two  cutting  heads,  s.  Jn  the  present 
example,  these  cutters  are  arranged  for  tongueing  and  grooving 
the  opposite  edges  of  the  flooring  deal,  as  is  Usual  in  laving  floor- 
ing. Thus,  in  the  elevation,  fig.  1,  the  two  square  cutters,  22, 
take  oft' the  two  angles  of  one  edge  of  the  deal,  having  the  central 
feather  or  tongue   standing  up,  whilst  the  other  double  anguuir 


TIIK   1 


,ia«W   r  .  off  th.   *liarp  anglea  from  i!.< 

A.'-      •••    .iv-i!--   •  -iv.r   baai,  f.T  DM   OBMf   ■VJe.eanMi   !!,•..• 

(4ai«  r»n:r»I  -r—.m-  <  ,-l.r.    .1    !•:    pf-U;    „•  lh<    plain   groove, 

angu- 

20.  ■•  aabaaktcd   to  Um  artiua  of  the  roU 
aaaaav,"  L,  for  bringing  lit*  upper  net 

aod  npaaluiag  the  thirkoaaa  of  the  deal,  wax  -  Jn*n 

sogh  Um  mprM't  in  •  finished  state. 


nan  :..-    . 


SE  FOR  PI 

LMPLB  PLATE  Q. 

TV  ■  '  In  P"*1 

epessim  nil  iilinn,  mil  then  in 
log  good  atikl 

: 

-  .n  longitudinal  section  on  a 
Largvr  •  rtion — 

.  body  of  the  machine 
eonaiata  of  an  l-iron,  which  is 

h  irizon- 

tal  trail  ' .  c,  arc  pawl  thro  I 

■ 

a  by  the  revol 
l  third  ipor-v 

\  ild  the  diametrically 
:  parall.-l  rail  ban,  l,  which  form  the  Hit  a. 
tag  fran 

whole  nf  the  action, 
■-■une  central  wheel,  c,  alio  drivel  al 
of  aimi 

har  <>n   I  lard,  *, 

i    roller 
I  :  bat 

washing  movement  a-  plane,  and   Um 

adjusted   to  fl  lo    be 

rltau"  ■ 

1 1 

a.  an  ! 

i  is  again  downward*. 


a,  and  theno- 

• 
■  .r..  j.     It  tlun  rate 

paaaad  round  Mm  be 
l,  from  the  n; 

finally  n 

•  and  is  then  | 
. 
paaaea  ever  Um  ■.  and  is  finally 

\- 
bowi  nader  treatment,  U 

follow  lie 


POWER-LOOM. 

i:  Z  a  M  P  I.  B    P  I.  A  T  B    H- 
We  ! 

■ 

tinting  iip^n  tlie  main  framing.    The  loon  ■  tl 
Mr.  William  Millignn,  of   Bradford,  who  baa  acoornpUaned  in  it 
the  dot  :  putting  any  nombet 

•  whilal  the  namber  ol 

tion  with. oil  thi  n  of  the 

-T. ill  Ixar.  without  involving  any  anevenneaa  in  the 
ill  friction  o 
that  it  will  neither  -!i|i  nor  (ray  the  cloth,  at 
-  dry. 

n  of  the 

1 n  in  working  order,  looking  on  tl laking-up 

idinal  or  front 
: 
carried  on  a   spindle   rappoited  in  a  alol   i'.   I 

■  -pur-win il.  n.  outaide  the  fi 
•  i  the  pinion,  c    Tli  - 

I  Um  wheel,  n,  nn.l  tnorea  along  with  this  wh< 
-  in   gear  with  a  pinion,  a,  carried  ronnd  along  with  the 
On  el,  r.     Inn 
upon  the  fabric  in  1 1 .  n,  and  with  its 

upportod  in  v. : 
tal  rod,  it.    Thia  r.O.  a*  it  I 
cloth  on  the  I- 
additional  fold  I  -  tin-   bl  am  t 

I  -pin  He  of  the  I'loth-lx  inn   has 

. 

Inclination  with  the  n  d  behind  the  rod,  11.    This 

it,  to  which  pin  i*  Job  ■ 

I  p  am,  with  tl" 

one  end  of  the  tappet-shaft,  M. 


BOOK   OF    INDUSTRIAL   DESIGN. 


When  the  loom  is  in  action,  as  the  horizontal  rod,  h,  of  the 
cloth-beam  gradually  rises  from  the   accumulated    folds  of  the 

cloth  beneath  it,  it  presses  against  the  inclined  side  of  the  lever,  I, 

raising  it  by  degrees  to  ■  vertical  position.     By  this  action,  with 

every  slight  advance  of  the  lever,  I,  towards  the  vertical  line,  it 
thus  pushes  back  the  lever,  K,  by  the  intervention  of  the  connect- 
ing-rod,  j,  so  as  to  shorten  the  extent  of  the  traverse  of  the  lever, 
K.  The  latter  lever  works  loose  in  a  fixed  stud  ventre,  n,  in  the 
side-frame,  and,  thus  suspended,  it  is  connected  by  its  straight 
pendant  end,  or  lower  arm,  with  the  wheel-work  which  we  have 

just  described,  and  by  its  back  angular  arm,  with  the  eccentric 

tappet,  L,  on  the  same  shaft  as  the  ratchet-wheel,  r;  and  outside 
this  wheel  is  set  the  regulator,  o,  the  lower  eye  of  which  turns 
loosely  on  the  ratchet. shaft  as  a  centre.  This  regulator  is  simply 
a  slotted  lever,  having  a  sliding-pieee,  F,  set  to  move  up  and  down 
in  the  slot  :  and  at  its  upper  end  is  a  short  collar,  acting  as  a  bear- 
ing for  the  upper  end  of  a  screwed  spindle,  q,  the  lower  opposite 
end  of  which  is  passed  through  a  screwed  hole  in  the  sliding- 
pieee,  P.  In  this  way  the  sliding-pieee,  p,  answers  as  a  nut  for 
the  screw,  q,  and  the  turning  of  the  screw  consequently  allows  of 
the  raising  or  lowering  of  the  nut  or  slide-piece  at  pleasure.  To 
the  top  of  the  regulator  are  hinged  three  detents,  s,  each  of  which 
takes  into  the  teeth  of  the  ratchet-wheel,  f.  On  first  setting  the 
loom  to  work,  the  height  of  the  slide-nut,  P,  of  the  regulator,  is 
first  adjusted  to  suit  the  required  number  of  picks  to  be  laid  into 
tho  fabric  per  inch,  and  the  regulator  and  lever,  I,  are  pushed 
forward  by  means  of  the  lever,  K,  as  far  as  the  rod,  H,  will  permit. 
When  the  loom  is  put  in  motion,  the  eccentric.  L,  during  one-half 
of  its  first  revolution,  presses  against  the  projecting  angular  end 
of  the  lever,  k,  and  pushes  it  out  to  an  extent  equal  to  its  eccen- 
tricity,  whereby  the  regulator  is  drawn  hack,  to  a  corresponding 
extent,  by  the  connecting-rod,  s,  whilst  the  detents,  R,  bring 
round  the  ratchet-wheel,  F.  During  the  remaining  half  of  the 
revolution  of  the  eccentric,  the  angular  tail  of  tho  lever,  k,  de- 
scends as  far  as  the  then  degree  of  elevation  of  the  cloth-beam 
rod,  H,  will  permit,  and  the  detents,  R,  are  raised  out  of  their 
position,  and  lifted  as  many  teeth  back  as  is  equal  to  the  distance 
retraversed,  the  three  detents,  T,  suspended  from  the  centre  of 
the  wheel,  B,  serving  to  hold  the  ratchet-wheel  fast  whilst  this 
change  occurs.  It  will  thus  be  seen,  that  whilst  the  detents,  R, 
are  always  drawn  the  same  distance  during  one-half  revolution  of 
the  eccentric,  tho  distance  to  which  they  are  returned  in  the  other 
half  revolution  must  be  less,  as  the  cloth-beam  rod,  H,  is  raised 
higher  by  the  winding  on  of  the  cloth.  The  lever,  I,  should  be 
parallel  with  the  slots  in  which  the  rod,  H,  works,  when  the 
projecting  end  of  the  lever,  k,  is  elevated  to  the  top  by  the 
eccentric,  L,  and  it  should  rest  on  the  rod,  n,  when  the  eccentric 
is  down. 

At  o  is  a  short  lever  connected  with  the  weft-motion  of  the 
loom,  which  lever  raises  tho  detents,  T,  by  means  of  a  chain,  off 
tin'  ratchet-wheel,  to  stop  the  movement  when  the  weft  breaks. 
The  lever,  r,  is  fast  on  one  end  of  the  horizontal  rod,  v,  on  the 
other  end  of  which  is  a  balanced  lever,  worked  by  the  weft  thread, 
on  the  principle  of  the  ordinary  well-known  weft-stopping  ap- 
paratus. 


DUPLEX   STEAM  BOILER. 

EXAMrLE  TLATE  0- 

This,  our  ninth  example  plate,  illustrates  a  most  effective  style 
Of  treatment  of  S  stationary  steam  boiler,  its  seating  and  mountings. 
In  these  views  tiie  convex  and  concave  rounds  are  well  brought 
out,  and  considerable  relief  is  given  to  the  furnace  doors  and  boiler 

ends  by  the  judicious  employment  of  Bhadows.  The  water  in  the 
sectional  view,  and  more  especially  the 
brickwork  in  the  elevation,  supply 
materials  for  the  development  of  the 

picturesque;    and    the   plate,   upon   tho 
whole,  is  a  fair  type  of  a  class  of  work 


h 


in  which  a  good  display  is  made  without  much  elaboration.  Tho 
boiler,  which  is  the  production  of  Messrs.  Bellhouse  &  Co.,  of 
the  Eagle  Foundry.  Manchester,  is  of  the  duplex  or  "  twin"  kind  ; 
that  is,  two  distinct  steam  generators  are  combined  together,  to 
work  as  one  boiler,  the  two  being  placed  side  by  side,  with  a 
central  tubular  chamber  between  them.  It  is  this  intermediate 
flue  which  forms  the  distinguishing  feature  of  the  contrivance,  the 
smoke  and  heated  air  from  the  two  generators  being  passed 
through  this  chamber,  on  4>cir  way  from  their  respective  furnaces, 
to  the  chimney. 
Fig.  1,  on  the  plate,  is  a  front  end  elevation  of  the  duplex 

boiler,  as  erected  in  brickwork;  fig.  2  i-  a  transverse  vertical 
section  corresponding,  the  section  being  taken  through  the  two 
furnaces,  the  brickwork  and  Hues,  and  the  overhead  steam-chest; 
tig.  3,  the  wood  engraving  in  the  body  of  the  description,  is  a  lon- 
gitudinal section  ,,f  the  arrangement,  taken  through  Ihe  inter- 
mediate chamber,  the  external  flues,  waterways,  and  the  stCI  in- 
chest :  and  fig.  4  is  a  sectional  plan  to  correspond.  Both  these 
latter  views  are  drawn  to  a  scale  of  one-half  the  corresponding 
views  in  the  plate. 

The  two  boilers  or  generators,  a,  are  of  the  common  cylindri- 
cal, tubular  class,  with  internal  furnaces  and  flues.  B,  running  ri  [hi 
through  them  from  end  to  end.  Tiny  are  set  in  a  brick  founda- 
tion, c,  suitable  flues  being  formed  in  the  walls  id'  brickwork,  to 
answer  for  the  special  arrangements  of  the  combination.  Each 
boiler  is  fired  separately,  through  the  usual  end  furnace  doors,  D, 
and  the  gaseous  products  pass  off  from  each  set  of  furnace  bars  in 
the  direction  of  the  arrows,  the  two  currents  meeting  .and  forming 
into  one,  in  the  main  end  transverse  flue,  E,  in  the  brickwork. 
This  combined  current  then  turns  again  towards  the  front  of  the 
boiler,  passing  directly  through  the  intermediate  chamber  oi  tubes, 


TilK    I 


rfc  baae. 
.<!i:-h   eroae    lh<-    anj. 
'.  r-afara,  Uing  open  »i  earh  mJ  into  the  reeperU 

I 
■ 
■  rmediale  chamber,  impart* 
■ 

|u»«iii^  away  <>f  the  »l«-am. 
Boo,  i,  passing 


til 


■ 

part,  tli- 

I,  r,  and 

■ 
I 

'  le  run* 

'■'■ 

of  the 

■ 

0in  central  . ' 

i 

•  generator*.  I 


•  ■  jnuj»    ail   Uio 
advantage*  uf  an  inti  ...  <n  each. 


WRECT-ACTING  M  \U!\i:  ENGINEa 

*nii-»  -liading.     The 

imp  and 

NlUlll    tx 

in  t lii-i 

The   /'  //  ■  'lich  thoae  engine*  arc 

I 

finu  a-i 

•  !.  ngth  U  I  i 

■ 

- 
re  ud  iii'i  tbi 
other — ' 

(KTllpV    ■ 

We  hi 

•    and   rivet  ;  .mil  the 

Mi  «.   v. 

— of   III.     /»  lulialf  of    lli 

lie  i 

'.i  ;  whiUt  nil  U 
thai  tin  one  i 
tber.     For  ii  - 
■  action,  not  uncommon  in  old  oadllatore,  i 

■ 

I 
lli-r  owner,  Captain  K 

C   uiilrv  ;  nn.l  | 

I 

■ 

■    C I 


BOOK   OF    INDUSTRIAL   DESIGN. 


CHAPTER   XV. 

DRAWING  INSTRUMENTS 


"A  good  workman  never  complains  of  his  tools," — although 
a  very  ancient  proverb,  and  having  a  poet  for  its  advocate,  is, 
nevertheless,  one  which  is  very  commonly  used  in  an  incorrect 
sense,  if  it  is  not  indeed  untrue  in  all  its  applications.  It  is 
certainly  a  very  usual  thing  for  a  bad  workman  to  throw  the 
blame  of  his  inefficiency  on  his  tools;  but  it  is  quite  as  certain 
that  a  good  workman  will  not  work  with  any  but  the  very  best 
tools.  The  draughtsman,  then,  who  aims  at  excellence  and  accu- 
racy in  his  mechanical  delineations,  must  not  only  possess  himself 
of  first-rate  mathematical  instruments,  but  he  must  preserve  them 
in  perfect  order. 

The  varieties  of  drawing  instruments  are  extremely  numerous. 
We  shall,  however,  confine  our  illustrations  to  such  as  are  of  more 
recent  invention,  or  more  improved  construction. 

A  Kad  pencil  needs  no  description.  But  the  form  to  be  given 
to  its  working-point  is  a  very  important  subject  of  consideration. 
For  drawing  straight  lines  wit'i  the  assistance  of  a  straight  edge, 
thi-  point  should  be  flat,  and  slightly  rounded.  Such  a  point  pro- 
duces as  fine  a  line  as  a  conic-al  point,  whilst  it  is  much  stronger, 
and  preserves  its  integrity  for  a  longer  time.  This  point  may  also 
be  used  in  describing  circles  of  large  diameter,  but  small  circles 
require  a  conical  point. 

Messrs'.  Marion,  of  Regent  street.  London,  have  registered  a  very 
ingenious  little  instrument  for  sharpening  lead  pencils  and  crayons. 
Our  engraving,  fig.  1,  represents  a  side  elevation  of  the  tool  in  the 
act  of  sharpening  a  pencil.      A  projection,  a,  is  formed  on  the 

side  of  a  piece  of 
Fis-  '•  metal,  sufficiently 

large  to  allow  of 
a  conical  aper- 
ture, b,  corre- 
sponding with  the 
required  cone  of 
a  pointed  lead 
pencil.  One  side 
of  this  projection 
is  slotted  to  re- 
ceive the  cutting  edge  of  the  small  knife,  c,  which  is  attached  to 
the  inclined  portion,  d,  of  the  metal  block  by  the  screw,  E,  passing 
through  a  slot  in  the  knife.  A  short  projection,  F,  is  formed  upon 
the  knife  for  the  convenience  of  adjustment,  and  when  sit.  it  is 
held  in  position  by  the  two  set-screws,  g.  A  small  handle  is 
screwed  into  the  block  at  H,  from  behind,  for  the  convenience  of 
holding  the  instrument  when  in  use,  and  the  end  of  this  handle  is 
hollowed  to  receive  the  small  projection,  f,  on  the  knife,  c,  for  the 
facility  of  holding  it  when  detached  for  the  purpose  of  sharpening 
the  edge.  An  adjustable  guide,  I,  is  secured  by  the  pinching- 
screw,  j,  by  one  end,  beneath  the  block,  and  is  furnished  with  two 
arms,  k.  jointed  on  to  the  end  of  the  rod  of  the  guide,  for  em- 
bracing the  pencil,  l,  during  the  cutting  operation. 


In  using  this  instrument,  the  pencil  is  simply  passed  In  [ween 
the  two  guide-arms,  K,  and  its  end  is  inserted  in  the  conical  hole,  n. 
It  is  then  turned  round  between  the  finger  and  thumb,  and  the 
knife-edge  coming  into  contact  with  the  end  to  be  sharpened, 
quickly  pares  off  the  material.  By  this  simple  apparatus  an  ex- 
cellent poiut  is  given  to  the 'pencil  in  a  very  short  time,  saving 
the  draughtsman  from  all  the  troubles  and  inconveniences  of 
blunt  penknives  and  fractured  lead. 

A  mathematical  drawing-pen  consists  of  a  pair  of 
flat,  tapered  steel-blades,  fixed  to  a  handle  of  ivory  ''•5,  2- 

or  ebony.  The  ink  is  contained  between  the  blades, 
and  flows  out  from  between  the  points,  the  thickness 
of  line  produced  being  dependent  on  the  distance 
asunder  of  the  points,  which  distance  is  regulated  by 
a  pinching-screw.  In  order  to  maintain  a  uniform 
thickness  of  line,  care  must  be  taken  to  clean  the 
outsides  of  the  points  after  each  fresh  supply  of  ink. 
It  is  often  necessary  to  draw  a  number  of  lines,  of 
different  thicknesses,  immediately  succeeding  each 
other.  In  this  case,  the  inconvenience  of  repeatedly 
turning  the  adjusting-screw  of  the  pen  may  be 
avoided  by  using  a  pen  of  the  construction  repre- 
sented in  figs.  2  and  3.  This  pen  is  the  invention  of 
M.  Maubert,  a  French  engineer,  and  differs  from  the 
ordinary  drawing-pen  in  the  shape  of  the  points,  g,  A, 
of  which  fig.  3  is  an  end  view.  These  points  are 
made  broad  and  rounded,  and  are  bent  at  the  sides, 
so  as  to  present  convex  surfaces  towards  each  other ; 
in  other  words,  they  touch  each  other  at  their 
centres,  but  aie  gradually  more  separate  towauls 
each  side ;  and  in  using  the  pen,  if  a  fine  line  is 
wanted,  it  is  held  vertically  ;  if  a  thick  line  is  needed, 
it  is  inclined  moro  or  less  to  either  side,  so  as  to 
bring  the  more  separated  portions  of  the  acting  edges 
in  contact  with  the  paper.  With  the  exception  of 
the  shape  of  the  points,  the  pen  represented  in  fig.  2 
may  be  taken  as  an  example  of  the  best  construction 
of  a  mathematical  drawing-pen.  The  blades  are 
formed  of  a  single  piece  of  well-tempered  steel,  and 
are  lived  upon  an  ivory  handle,  by  means  of  a  brass 
socket.  In  si. me  pens,  the  tips  only  of  the  blades 
are  of  steel,  tho  remainder  being  of  German  silver,  or 
of  brass, ;  and  one  blade  is  jointed  at  its  root,  so  as 
to  be  capable  of  being  opened  out  ami  cleaned,  when 
necessary.  A  spring  is  fixed  between  the  blades, 
so  as  to  keep  them  open  as  far  as  the  regulating  screw 
will  admit.  Whilst,  on  the  one  hand,  this  facility  in  cleaning  is 
an  advantage  ;  on  the  other,  there  is  an  accompanying  lial 
the  joint  getting  loose,  in  which  case  the  points  can  never  be  kept 

opposite  to  each  other,  and  it  is  quite  impossible  to  preserve  uni 

2  a 


Fig.  3. 


. 


f  r- 


and  rlranaaa  of  !u      . 

utfn*.  and 

T>.  .  t:i..i.!jr»'...n  ■•(  !..•■  Mmm    :i   ilraain^pra   la  II.'   hwrtili    n  r.f 

- 


tin*  !;»••  :•  arai 
graap  of  tbe  f.  ■ 

■part  ■ 

■ 

!        .  •  .  ■■ 

■a  the 

■ 

■ 

i 
■ 

- 

drawiiv 

;  -dace  a   lir  • 

rdinary 

■ 

I  variation,  iw 
•  «raall  acalc ;  I 

n.vi-««arj-  rhangra,  « 

b 


r  a  Ua:.«\.  r- 

I  »t«-t-l  atud,  rm-lcd  U>  thi   |  lat.-.  e.  and  of 
conajderaUc  diameter,  fur  Un  ■>..;..  •  •:  ale  idinaaa 

■ 

down  i 

and  fall.     T:  ■ 

that  an; 

■ 

-1  aa 
fp>m  a  K-ali- ;  aril  a 

■  ■fa  |>air  of  I  I,  and 

.nd  a 

■ 

l 

.  an  nnplcaau  I 

tr.'m  all  cn>a»    ; 
lateral  looat-ncaa.      The  moat  ordinary  kit 

■ 


BOOK   OF   INDUSTRIAL  DESIGN. 


181 


»nea  riveted  together.     The  better  kind  have  a  steel  pin  passed 
through  the  leaves  of  the  joint,  upon  which  a  flat  brass  or  other 


metal  nut  is  passed,  at  the  further  side.  This  nut  has  two  small 
holes  upon  its  face,  for  the  introduction  of  the  points  of  a  turn- 
screw,  to  be  met  with  in  most  sets  of  instruments.  The  joint- 
leaf  of  one  leg  of  a  pair  of  compasses  is  usually  of  steel,  as  this 
arrangement  gives  a  smoother  action  than  when  both  sides  of  the 
joint  are  of  the  same  metal.  The  better  kind  are  also  made  with 
two  steel  leaves  on  one  side,  which  are  introduced  between  three 
brass  ones  on  the  other  ;  but  some  have  only  one  leaf  on  one  side, 
and  two  on  the  other.  A  perfect  compass-joint  is  a  thing  seldom 
met  with,  and  draughtsmen  are  continually  subject  to  annoyance, 
arising  from  the  inequality  of  action  of  the  joints  of  their  com- 
passes. After  some 
Fib-  8-  little     usage,    these 

parts  invariably  im- 
bibe the  bad  habit  of 
an  alternate  tightness 
and  looseness,  so  that 
w\icn  the  screw  is  adjusted  to  tighten  the  joint  for  one  part  of 
its  movement,  the  objectionable  slackness  is  only  removed  at  the 
expense  of  an  equally  provoking  stiffness  in  another  part.  Messrs. 
Bentley's  "spiral  spring  compasses"  aim  at  remedying  this  evil, 
by  the  adaptation  of  a  small  coiled  spring  to  the  joint,  in  such  a 
manner  as  to  equalize  the  pressure  of  the  frictional  surfaces 
throughout  the  entire  movement.  Our  sketch,  fig.  8,  which  re- 
presents a  side  view  of  the  end  of  the  centre  joint  of  the  compasses, 
explains  the  mode  of  application  of  the  spring.  The  centre  joint, 
A,  which  is  sectioned  to  show  the  spring,  has  a  recess  bored  out  of 
one  side  of  it,  just  large  enough  to  receive  the  short  coiled  spring, 


Fig.  9. 


b.  When  this  centre  joint  is  inserted  between  the  two  eyes 
forming  the  outer  joints,  the  spring  reacts  from  the  bottom  of  its 
box  against  one  of  the  eyes  or  cheeks  of  the  outside  joint,  thus 
keeping  up  a  regular  smooth  working  pressure  on  tho  joint  surface- 
Externally,  this  little  modification  in  no  way  affects  the  appear- 
ance of  the  instrument,  as  the  spring,  being  entirely  embedded  in 
its  recess,  is  not  seen.  At  a  mere  tritle  in  the  increase  of  the 
cost,  an  important  objection  is  hero  remedied  by  very  simple 
means. 

Some  dividers  are  made  with  one  of  the  legs  so  fitted  as  to  be 
capable  of  a  slight  adjustment  independently 
of  the  main  joint.      These  are  called  "hair 
dividers,"  and  are  represented  in  fig.  9.     The 
leg,  A,  is  not,  like  tho  other,  soldered  to  the 
shank,  but  is  formed  with  a  long  thin  strip  of 
metal,  which  lies  in  a  groove  on  the  inside  of 
the  shank,  and  is  fixed  to  the  latter  by  a  screw, 
at  its  upper  end,  near  the  compasses  joint. 
This  thin  strip  acts  as  a  spring  to  bring  the 
point,  a,  nearer  to  the  point  of  the  other  leg. 
A  screw,  b,  passed  through  the  shank,  adjusts 
the  point,  A,  a  slight  distance  in  or  outwards, 
thus  affording  a  means  of  taking  measurements 
more  minutely  accurate  than  with   the  mere 
direct  action  of  the  hand  upon  the  main  joint. 
Our  fig.  9  may  be  taken  as  the  representation 
of  a  very  excellent   style  of  dividers.     The 
point  should  be   strong,  and  not   too   finely 
tapered,  and  they  should   meet  when  the  in- 
strument is  closed. 

All  sets  of  instruments  contain  a  large  pair 
of  compasses,  in  addition  to  the  dividers,  which 
is  usually  of  similar  construction,  except  that 
one  of  the  legs  is  made  to  fit  into  a  socket  in 
the  shank,  and  a  pencil  or  pen  may  be  substi- 
tuted, as  required.  The  pencil-holder  and  pen 
are  both  jointed,  so  that,  in  every  case,  they 
may  be  put  in  the  best  position  for  action.  In 
the  better  kind, the  fixed  leg  is  also  jointed;  so 
that  in  describing  circles  of  large  diameter,  the 
centre  point  may  still  be  entered  vertically  into 
the  paper.  A  lengthening  bar  is  also  provided,  which  can  be  fitted 
into  the  shank-socket,  whilst  the  pen  or  pencil  can  be  placed  at 
the  end  of  the  bar,  thus  giving  the  compasses  a  greater  range. 

In  fi"s.  10  and  11,  we  have  represented  a  modification  of  this 
instrument,  of  German  invention.  This  tool  has  no  separate 
pieces,  but  is  so  arranged,  that  a  pen,  pencil,  or  point,  may  be 
brought  into  action  as  desired.  The  shanks  are  forked,  and  the 
leg  pieces  are  jointed  to  their  extremities.  One  of  the  leg  pieces 
is  formed  with  a  steel  point  at  one  end,  and  a  pen  at  the  other ; 
whilst  tho  other  leg  has  a  steel  point  at  one  end,  and  a  lead  pencil 
at  the  other.  The  legs  are  jointed  to  the  shanks  by  their  longi- 
tudinal centres,  and  can  be  turned  between  the  fosksj  so  as  to 
bring  into  action  whichever  end  of  the  leg  is  required.  A  small 
pinching-screw  is  passed  through  one  side  of  the  shank,  near  its 
extremity,  to  fix  the  leg  in  position. 


I" 


what    muller    : 

■ 

.1     in- 

AnntliiT     form     of 

• 

-  U  a  tpock- 

.  t."  or  "  turn  in  "   BOm- 

■  -   up   a 

II  s|  :u-f  when 

-  n   iTOM  uec- 
n   at    the   lino 

1— -2.  ill  ' 

••nl  mid 

n  -  of  the  in- 
■tnunent    when    fully 

oonatrooilon,    ami     in 

il  unliko 
rmu    pair   ju»t 
'. 
I    :li.ir  lower   i 

points, 
tl  .in  at  th.ir  extremi- 

.t    their 

:   round   into  « 

\  r  fixing 

In  tin'    German    Instniment, 
I 
i  tin-  upper  ondi  ol 
■hown  in   the    •  I  i.   iiinl  in   Umm 

. 
a»  in  fig.  it.    When  in  th  - 

ami    |-  !.  .  i'liin   tlir   fori 

• 

'v  draw- 

,  tli.  in  from    i 

\\  •■  variuu* 

peeeee  of  a  n 
N 

.  t  ■  -r   the 
•  umbroua 


■uuallrr  and  ■ 

-   a   fruiit.  aii.l  fig.   18  a  ado 
■       '    ' 
]  IBM,    to 

which   a   unall   han.l  I. 

it       It   « 

bold   l'T  a   Mnall   enjww,  in   a   Mekal    formed   in   the   tag  of    Ihe 

•  nt      'llii*  ar.  ids    a    m.  aim    of  adj 

as  to  length,  whilat  I 
dentalrj  I     opnaaei  of  the  lar.--  i 

■ 
Imnghtamen  m  in  tin m,  if   the  u 

not  im'..  point)  which,  from  its  greater 


Fif.  IS. 


F.,-.  14. 


■  injury. 

I 

of  nn 

instrument    | 
himil.ir  to  tin- 

<vpt  thai  it  haaa  pen- 
ril  in-' 
I 

qulra  to  In.  adjoated  t..  any  desired  ra.iiu«.  by  uV 
the  ham I.     In  «.rk  whi  re  gfl 
for,  it  will   often   !*•  foiin.l  I  i  a  linn 

ndjnatmenl  In  thii  manner,  particular!;  if  the  Jolnhi  of  tbi 

mint  i.  ■  ["hla  difficulty  la  go! 

over  In 


BOOK   OF   INDUSTRIAL  DESIGN. 


Fig.  20  is  a  side,  and  fig.  21  a  front  view  of  a  pair  of  pen  com- 
passes of  this  class.    The  use  of  such  instruments  is  confined  to 


Fig.  IT.         Fig.  18. 


Fig.  20. 


very  small  circles,  of  half  or  three  quarters  of  an  inch  in  radius  at 
the  most.  In  the  example  we  have  selected  for  illustration,  the 
emtio  leg  is  of  brass,  or  German  silver,  and  is  in  one  piece  with 
the  milled   handle.      It  is  also   provided 

with  a  needle  point.     The  pen  is  made 

with  a  spring-tempered  steel  shank,  K, 
which  lies  in  a  groove  cut  in  the  centre 
leg,  or  body,  and  which  is  fixed  to  the 
latter,  at  its  top,  by  a  screw.  A  small 
screw  spindle,  L,  is  passed  through  an 
opening  in  the  pen  shank,  and  is  jointed 
to  the  centre  leg,  and  a  button,  or  nut, 
is  passed  on  to  the  screw  spindle  outside 
the  shank.  This  pen  shank  is  so  fixed 
as  to  have  a  tendency  to  stand  out  from 
the  centre  leg  to  the  full  extent  of  the 
instrument's  range,  and  by  turning  the 
button  of  the  screw,  L,  it  may  be  forced 
in  or  allowed  to  open,  so  as  to  give  the 
necessary  adjustment.  Fig.  22  is  a  side 
elevation  of  a  pair  of  slightly  modified 
spring-and-screw  compasses  ;  it  is  shown 
with  a  Socket,  carrying  an  engraver's 
burin.  An  i/ory  handle  is  fixed  to  the 
centre  leg,  or  body  of  the  instrument ;  and 

this  arrangement  is  considered  by  some  artists  to  give  greater 
control  over  its  action.  The  commoner  kind  of  spring  bow  com- 
passes consists  of  a  single  piece  of  steel  forming  the  two  legs,  and 


Fig.  22. 


having  a  small  brass  handle  attached.  The  steel 
of  the  legs  is  so  tempered  as  to  give  them  a  ten- 
dency to  stand  apart,  and  the  radius  distance  is 
regulated  by  a  screw  in  the  same  manner  as  in  the 
instruments  represented  in  figs.  20,  21,  and  22. 

The  draughtsman  lias  frequently  to  delineate 
circles  of  a  radius  far  exceeding  the  range  of  ordi- 
nary compasses,  and  for  this  purpose  he  must  pro- 
vide himself  with  "beam"  compasses.  A  good 
form  of  this  instrument  is  represented  in  side  eleva- 
tion, in  fig.  23,  and  in  transverse  vertical  section, 
in  fig.  24.  It  consists  of  a  wooden  bar,  or  ruler, 
T,  of  considerable  length,  and  of  a  X  section,  being 
formed  of  two  strips  united  by  a  dovetail  joint. 
This  construction  prevents  warping  or  bending, 
and  is  necessary  where  a  scale  is  cut  on  the  bar,  as 
any  deviation  from  a  straight  line  would  render  the 
measurement  inaccurate.  The  compasses  are  pro- 
vided with  a  pen,  or  pencil  leg,  and  a  centre  leg, 
these  being  fitted  upon  the  bar  with  socket  pieces, 
M,  m'.  These  socket  pieces  are  fixed  at  any  point 
along  the  bar,  by  pinching  screws  at  the  side. ;  but 
to  prevent  the  point  of  the  screw  from  injuring  the 
bar,  a  loose  plate  of  metal  is  interposed  next  to  the 
bar,  as  shown  in  the  section,  fig.  24.  The  socket, 
M,  is  in  a  solid  piece  with  its  pen,  or  pencil- 
holder  ;  but  the  centre  leg,  N,  is  in  a  separate 
piece  from  its  socket,  m',  and  is  capable  of  minute 
adjustment  back  or  forward  in  the  latter.  The 
socket,  m,  has  a  cylindrical  groove  along  its  under  side,  in  which 
slides  the   head  of  the   leg,  n.     This   head  is  formed  with  a 

Fig.  23.  Fig.  24. 


horizontal  serew  passage,  or  nut,  to  receive  the  screw  spindle, 
I,  which  is  held  by  an  eye  at  the  end  of  the  socket  groove, 
and    is   actuated    by    means   of   a    bultou    on    the   outside.      By 


1  • 


it  atvrary   at   any   part   of    the  an 

a.  i.  Ui—owl  »aJ   ~i  pretty  near  the  mark,  ami  fi\ 
.th  of  raJiu*  b  thea  obtained  by  adjusting  the  c* 
lij  aiiiai  iff  am  eoapaaar*. 

ai—i  what  <ifl.-r.-nt  dVexription,  are  represented  in  aide  alev»: 

t..-  M.     1:.  Uui  u.<tnu.i<  :.'..  ■Mat  b  amlir  >■  ..f  r.«  ul,  Uk-  onaln 


- 
■ 

ng  strew  underneath 
■ 
which  a  vernier  scale  it  rut,  so  thai 
may  lie  taken. 

filed  at  a  convenient  |  or  a-,  i  tin  n  tin 

which  carriea  the  moveable  ;  lock  or 

forward,  a*  ni  it— nr,  by  thi 
LS.  aaaj  .  r  «  -  «•  l 

Of  the  compasses  cjaaa  of  drawing-instruments,  there  now  re- 
main  to  be  •! 

meat  b  represented,  in  front  and  aide  elevation,  in  I 
Ita  nae  b  to  inrreaae  or  reduce  measurements  to  a 
to  that  of  the  original  drawing,  of  whk-fa  a  copy  is  being  made ; 
and  a  great  deal  of  time  may  be  aaved  1 
there  U  much  Ices  risk  of  making  mistakes  with  it,  than  « ' 
draughtsman,  in  rodncing  a  measurement,  has  first  to  take  the 
oVtaaea,  ni  bV  original  drawing,  in  bb  eommon  diridera,  and,  l>y 
applying  it  to  the  aeale  of  that  drawing,  ascertain 
arithmetically  ;  and  ti,  »rreapooding 

r., )•.*-.,!  swab,  mti  h  Im  baj  «.-.:•.  to  talu  in  i.:-  divide  ra,  -• aa  t.. 

>'• 
the  other  hand,  the  action  of   taking   the   measurement   on   the 
original  drawing,  at  one  end  of  the  instrument,  :. 
end  to  the  measiiruntnt,  aa  increaaed  or  reduce.'  I 
theoopy.     The  instrument  consists  of  a  eou; 
brass  plates,  connected   by  an   ad 

Tmitiea  of  each  pari 
lut,  if  th*.  joint.   : 

■ 
between  the  points,  at  carh  end.  will  he  equal ;  bag 
■  adjusted,  aa  in  the  | 
ride  U  only  half  that  • 
poinu  at  one  • 

-ace  will  be  measured 


jt  tha 
■    -  a/  the  same  proper- 

:!uU  which  is  ■**•■*• 

time   being,  between  the 

f  the  joint,  J.     To  enable 
..ughtanun  to  art  the  inatra- 
ment   I 

t  has 

an  iii  : 

-responding  to  the  desired 

uaaal 

- 

it.     Tlie   instrument    is   n. 

a  purpose*,  in  aJ.;i- 

>ine  end  is  .*.. 
radius  of  a  rii 

side  of  an  in~ 
ii 
inatnmtent  b   usually   grad 
-  purpose,  an«i 

tinding  the    ; 

The 

made,    and 
:.'>em ; 

DasaV  -v 

ation  than  the  prearrratinn  of  the 
time  is  freqn- 

ripal  ' 

;<irtial 

a  no<« 

in  a  brass  socket,  with  an 

handV  h  made  to 

•  and  uncovers  a  anaU  ecrew-drivcr,  which 


BOOK  OF  INDUSTRIAL  DESIGN. 


Fi?.  28 


will  serve  to  (urn  the  screw,  e,  or  any  of  the  smaller  screws  in  the 
other  instruments. 

In  treating  of  drawing  ellipses,*  we  have  already  described  one 
of  the  many  instruments  constructed  for  that  purpose. 
The  well-known  "  trammel "  is  one  of  the  simplest  in 
construction,  but  it  is  very  defective  in  practice.  In 
figs.  29  and  30  we  give  an  elevation  and  plan  of  a 
trammel  of  the  newest  and  most  improved  form,  in  which 
tho  practical  defects  aro  very  much  lessened,  but  the 
contrivances  by  which  this  approximate  perfection  is 
attained  are  of  such  a  nature  as  to  require  a  more  than 
ordinary  excellence  and  accuracy  of  workmanship  in  the 
construction.  The  trammel  consists  of  a  metal  bar,  r, 
on  which  are  fitted  three  sliding  sockets,  which  can  be 
adjusted  at  any  points  on  the  bar.  Two  of  these  sockets 
cany  centre  legs,  p,  o,  and  the  third  carries  a  pen,  or 
pencil,  s.  In  addition  to  these  details,  a  guide-plate, 
q,  is  required,  having  a  couple  of  grooves  cut  in  its 
upper  face,  at  right  angles  to  each  other.  This  guide- 
plate  has  two  short  pin  points,  on  the  under  side,  to 
prevent  it  from  slipping  on  the  paper  upon  which  it  is 
placed.  In  ordinary  instruments  the  legs,  o  and  p,  ter- 
minate in  simple  points,  which  are  respectively  caused 
to  traverse  the  grooves  in  the  guide-plate,  Q,  in  describ- 
ing the  ellipse.  It  is,  however,  found  to  be  almost 
impossible  to  obtain  a  smooth  action  with  this  arrangement,  as 
the  pressure  on  the  points,  being  oblique  to  their  line  of  move- 
ment along  the  guide-grooves,  the  friction  is  apt  to  be  irregular 
and  so  cause  a  varying  motion  of  the  pen  or  pencil  point,  and  produce 


an  uneven  outline.  In  (lie  instrument  represented  in  fi.'s.  -29  and 
211.  the  parts  which  trav..rso  the  guide-grooves  in  the  plate,  q,  COD- 
siM  of  small  steel  wheels,  o,p,  carried  in  the  forked  ends  of  the 


1  See  page  17. 


steel  spindles,  o',  p',  which  are  entered  loose  into  the  socket  legs, 
o,  P.  Thus,  whilst  the  wheels  considerably  alleviate  the  friction 
arising  in  traversing  the  grooves,  they  always  maintain  their  posi- 


.  31. 


Fig.  32. 

tion  with  regard  to  the  grooves,  whatever  he  the  position  of  the  bar, 
it,  and  pen,  s.  In  adjusting  the  instrument,  it  is  simply  necessary 
to  set  tho  pen  and  centre  legs,  so  that  the  distance  of  the  two 
latter  from  the  former  shall  correspond  respectively  with  the 
semi-transverse  and  semi-conjugate  axes  of  the  ellipse  to  be 
described.  With  the  instrument  represented  in  the  engravings 
it  will  not  be  possible  io  describe  any  ellipse  which  does  not  lie 
wholly  outside  the  guide-plate,  q;  and  where  smaller  ellipses  aro 
required,  a  smaller  guide-plate  must  be  used. 

Beyond  comparison,  the  best  instrument  we  have  seen  for 
drawing  ellipses  is  that  invented  by  Mr.  Webb,  and  represented  in 
e'cvation  in  fig.  31,  and  in  plan  in  fig.  32.  It  consists  of  a 
lozenge-shaped  table,  a,  of  thin  metal,  supported  upon  four 
pointed  legs.  a'.  Two  parallel  guides,  b,  are  fixed  across  the  top 
of  the  table,  a,  and  a  disc,  c,  is  fitted  between  them,  in  such  a 
manner  as  to  be  just  capable  of  turning  and  sliding  between  tho 
guides,  b.  The  disc  has  a  slot  at  one  side,  extending  from  tho 
centre  to  the  circumference,  and  in  this  is  fixed,  a(  any  point,  by  a 
screw,  d,  a  spindle,  E,  passing  down  through  the  table,  a,  below 
which  it  has  fixed  to  it  a  slight  frame,  F,  carrying  a  screw  spindle 
c.  This  screw  serves  to  adjust  the  pen,  or  pencil,  it,  back  or  for- 
ward, on  the  frame,  F.  The  spindle,  E,  works  in  a  slot,  i,  in  the 
table,  a,  which  slot  is  at  right  angles  to  the  disc  guides,  b.  The 
instrument  is  caused  to  operate  by  turning  the  spindle,  e,  by 
means  of  the  button,  D,  which  action  turns  the  carrier  frame,  f 
and  also  the  disc.  b.  It  then  follows,  that  if  the  spindle,  e,  were 
five  1  in  the  centre  of  the  disc,  B,  the  point  of  the  pen  would 
describe  a  circle.  If,  however,  the  spindle,  e,  is  fixed  eccentri- 
cally in  the  disc,  the  rotation  of  the  latter,  between  its  guides,  r, 
will  cause  the  spindle  to  traverse  the  slot,  1,  in  the  table,  a.  in 
such  a  manner  that  tho  point  of  the  pen  will  describe  a  perfect 


Tin:  i  mans 


«U*jmp.     la  f|~<"'3  the  Instrument,  two  !.:>•-•  are  draw  a 

are  placed  upon   theee  Uu«-% 

aiia  of 

•v  ■  lino 

l 

■     ■ 

.   II.   is 

aith  the 

pen,  ii, 
. 

\  apindlo, 

v  (hi  :i  bo  described.    Tho 

■  L  with  <  »l  j"ints 

ju-t  eufficil  »t 

the  act 

■    . 

I  overcome  tli<> 

:  ■      .        ■  : "    il,  to  touch  the 

'  J"int  ill 
ngth,  in 
perfectly  leveL 

i  rircli  -,  i->  the  ellipti- 
. 

■■  of  which  a  pencil-holder  . 
wild  a  tulmlar  locket,  »■>  as  •■  i  Ircubuiy 

pencil-holder  'n  jointed,  m  that  thi 

In  nalng 
older  U 
pUccd  in  the  centra  of  the  ellipse,  and  the  leg  ia  in 
■ 

are  held 
nix I  round  with  the 

iii,.n,  it 
U  necessary  ii  irrying  tho    pencil-holder  ihould   be 

thia,  om 
nching  out  "ii  on  .  or  on  both 

.  ami  til,' 

aa,  when 
tba  per- 

ir  position  al  I   thia   important 

ind  t'i  be 

make  .-. 

i.  »r  the 


■M-pante  elevation*,  tak,  n  at  right  angteo  to 

i  ■:.,   i'l   ■   all,"  I 

in    a    Lnuk.-t 


r ,  a. 


r«.M 


to  an 

V. 

die,  Hke  a  nut, 

Tliia 

and,  in 
v  tra- 

■  '..I.      \\ 'Ii,  ii    ■ 

of  the  tho  in- 

atnmv  nl  ia  ti. 

the  n  i  to  that 

in  which  it  waa  |wi-  • 

i.   Thia 

*  k   tin« 

from  whioh  it  alerted  ;   and 
when  tiii -  point  hi  reachi  d,  the 

to    the 

'  mil.  lit 

I  with  a 
pin,pro|i  c  ting  down  almost  to 
the  level  of  the  bottom  of  the 
dlac    It  !■-  all  ■    ■  nhonld  roll  arid 

form  pi  I     •   instrument  may  be   used   I  i 

. 

i  a  pur- 
■  ulii.li  Ihoopiai 
lucuilii  s.    Tho  usual  method 

de  it  into  a  inn  • 
or  brapexiuma — to  meaanre  Ifti 

of  lh<  ir  prod  ! 

■ 
tho  ealculati 
obviating  fanlta  in  tho  arithmetical  pari  "i  Ihe  worl 
by  takl 

■,  this  method 

amount  of  labour  of  an  Irkaome  kind,    Attempta  ! 
!  thia  by  entti 

' 
r,  of  determinal  hod — nt 

' 
■ 


v  mm 


BOOK     OP     INDUSTRIAL     DESIGN. 


Several  "  planimeters,"  or  instruments  for  mechanically  mea- 
snring  the  area  of  plain  surfaces,  -were  exhibited  in  the  Great 
Exhibition  of  1851,  and  are  noticed  in  Mr.  Glaisher's  admirable 
report  on  Class  X.,  "  Philosophical  Instruments,  and  pro- 
cesses depending  upon  their  use."  All,  or  nearly  all  of  these, 
aimed  at  the  solution  of  the  problem  by  integrating  the  dif- 
ferential expression  of  a  curve,  tra'ced  on  a  plane 
surface,  being  conceived  on  the  old,  and  now  almost 
forgotten,  view  of  the  differential  calculus,  which 
regarded  the  differential  of  a  magnitude  as  a  measure 
of  the  velocity  of  its  increase  at  any  instant.  Sup- 
pose a  straight  line  to  be  carried,  with  a  uniform 
motion,  along  the  base  line,  or  abscissa,  of  any  curvi- 
linear area,  remaining  always  parallel  to  itself,  and 
perpendicular  to  the  base  line,  and  that,  during  this  motion  a 
moveable  point  in  the  line,  so  carried,  is  always  kept  on  the  cir- 
cumference, or  boundary  line,  of  the  area.  Then  it  is  clear,  that 
the  velocity  of  increase  of  the  area  will  be  proportional  to,  and 
therefore  measured  by,  the  length  of  the  ordinate,  or  portion  of  the 
moveable  line  included  between  the  base  line  and  the  describing 
point.  Again,  a  disc,  or  wheel,  can  be  supposed  to  revolve  with 
an  angular  velocity  always  proportionate  to  the  same  ordinate  ; 
in  which  case  the  total  angle  of  revolution  described  by  it  will 
increase  by  similar  increments  with  the  curvilinear  area,  and  will, 
consequently,  always  be  proportionate  to,  aud  a  measure  of,  that 
area.  The  area  may  therefore  be  read  off,  upon  its  circumference, 
by  any  method  which  keeps  account  of  the  number  of  revolutions 
made  by  this  wheel,  which  may  be  called  the  integrating  wheel, 
disc,  or  roller.  If  the  circumferences  of  two  circles  be  connected 
by  teeth,  or  by  simple  contact,  so  as  to  work  together,  their 
angular  velocities  will  be  inversely  as  their  radii ;  so  that,  if  the 
radius  of  one  of  them  be  constant,  the  angular  velocity  of  that 
one  will  be  directly  as  the  radius  of  the  other.  Thus,  any  mecha- 
nical arrangement  securing  the  condition  that  a  roller,  or  disc, 
shall  be  carried  round  on  its  centre,  by  contact  with  a  uniformly 
revolving  circle  of  a  radius  always  equal  to  the  length  of  the 
variable  ordinate,  will  at  once  be  a  solution  of  the  problem.  The 
condition  alluded  to  may  be  obtained  by  employing  a  couple  of 
discs  at  right  angles  to  each  other,  or  by  using  a  cone  and  a  disc, 
with  their  axes  parallel  to  each  other.  The  former  construction 
is  adopted  in  one  or  two  instruments,  invented  by  continental 
mathematicians,  the  latter  by  Mr.  Sang  of  Kirkaldy. 

Mr.  Sang's  instrument,  which  is  represented  in  perspective 
in  fig.  35,  indicates  the  area  of  any  figure,  however  irregular, 
on  merely  carrying  the  point"  of  a  tracer  round  its  boundary ; 
and.  besides  the  advantage  of  not  injuring  the  drawing,  it  pos- 
sesses that  of  speed  aud  accuracy.  A  frame,  a,  carries  an  axle, 
which  has  on  it  two  rollers,  b,  of  equal  size,  and  a  cone,  c.  It 
is  heavy,  so  that  it  maintains  its  parallelism  on  being  pushed 
along  the  paper.  The  sides  of  the  frame  are  parallel  to  the  edge 
of  the  cone,  and  are  fitted  to  receive  the  circumference  of  four 
friction  rollers,  R,  which  move  along  a,  and  carry  a  light  frame,  f, 
terminating  on  the  tracing-point,  p,  to  which  the  handle,  H,  is 
attached  by  a  universal  joint.  The  frame,  f,  also  carries  a  wheel,  I, 
which,  by  means  of  a  weight,  is  pressed  on  the  surface  of  the 
cone,  and  receives  motion  from  it  as  the  tracer  is  carried  along  the 


paper.  The  index-wheel,  I,  only  touches  the  cone  by  a  narrow 
edge,  the  rest  of  its  circumference  being  of  smaller  diameter,  and 
containing  a  silver  ring  divided  into  200  parts,  which  are  again 
subdivided  by  a  vernier  into  2,000  parts.     The  value  of  each  of 

Fig.  36. 


these  divisions  is  the  TJ3tk  part  of  a  square  inch;  so  that  one  turn 
of  the  wheel  represents  20  inches.  Another  index  wheel,  t, 
moved  by  i,  is  divided  into  five  parts,  each  of  which  represents 
20  inches,  so  that  a  complete  revolution  of  T  values  100  inches. 
The  eye-glass,  e,  assists  in  reading  the  divisions  aud  vernier. 

It  is  apparent,  from  the  construction  of  this  instrument,  that  if 
the  tracer  be  moved  forward,  it  will  cause  the  index  to  revolve, 
not  simply  in  proportion  to  that  motion,  but  in  proportion  to  the 
motion  of  the  tracer,  multiplied  by  the  distance  of  the  edge  of  the 
index-wheel,  from  the  apex  of  the  cone;  and  that  the  revolving 
motion  of  the  index  will  be  positive  or  negative,  according  as  the 
tracer  is  carried  backwards  or  forwards.  Hence,  if  the  tracer 
be  carried  completely  round  the  outline  of  any  figure — on  arriv- 
ing at  the  end  of  its  journey,  the  index-wheel  will  show  the 
algebraic  sum  of  the  breadth  of  the  figure  at  every  point,  multi- 
plied by  the  increment  of  the  distance  of  the  points  from  the 
apex  of  the  cone  ;  that  is  to  say,  the  area  of  the  figure. 

This  instrument  possesses  great  simplicity  of  construction. 
Both  factors  of  the  continuous  multiplication  are  directly  trans- 
mitted  from  the  motion  of  the  tracing  point  in  the  simplest 
manner.  The  influence  of  the  elasticity  of  the  parts  of  the 
machine  ou  the  accuracy  of  its  indications,  may  lie  discovered 
by  moving  the  tracer  a  second  time  over  the  boundary  of  the 
figure,  after  having  turned  the  whole  instrument  round  180°. 
The  effects  of  the  imperfections  in  the  mechanism  will  now  have 
changed  signs,  and  one  of  the  results  will  probably  be  found  to 
be  a  little  too  large,  and  the  other  a  little  too  small.  The  average 
between  the  two  is  the  exact  area  of  the  figure,  and  is  more  to 
be  depended  on  than  the  results  of  measurements  made  by  scale 
and  calculation  in  the  usual  way.  A  careful  operator,  in  using 
the  planimeter,  will  always  take  the  average  of  two  tracings  in 
this  manner;  but  when  he  experiences  the  rapidity  with  which 
this  may  be  done,  he  will  find  the  trouble  as  nothing  in  com- 
parison with  the  harassing  labour  of  calculating  by  scale  and 
multiplication. 

Mr.  Miller,  of  Woolwich,  has  devised  a  very  useful  modifica- 
tion of  the  common  jointed  rule.  This  instrument  is  termed  a 
"radiator,"  and  our  engraving,  fig.  36,  represents  a  portion  of 
it  in  plan,  whilst  fig.  37  is  an  end  elevation.  The  inner  edges  of 
the  legs  are  used  as  rulers,  and  the  joint  has  a  transparent 

2b 


eeatre.  a.  which  is  placed  direct);  orer  the  pout  to  be  drawn  to. 
A  graJaatr  J  «.*.»  supplied,  at.  J  the  brmM  Irgs  are  furtu>hed 


r«  m 


with  m  .imit  of  an;  length  of  ruler  being  used. 

1  L-   r»:.j:   r  .«  a]  :  '    al  It  to  the  f  :.   wing  j  arm  -•  -  :— 

For  drawing  lines  in  perspective,  or  geometrical  drawing,  to  a 
pomt  or  cent:  off  angles  as  a  protract)-: 

right-angled  triangle,  or  an;  other  angles ;  and  for  setting  oat 
yolyguaw  of  different  numbers  of  sides.  In  using  it.  the  centre 
of  the  giaa  is  placed  over  the  centre  to  be  drawn  to.  and  a  line 
is  drawn  along  the  inner  edge  of  the  ruler  from  the  point  re- 
quired. When  man;  lines  are  to  be  drawn  to  one  centre,  the 
hand  must  be  placed  upon  one  leg,  to  allow  the  other  to  be 
moved  to  the  several  ; 

I  -mi  of  protractors,  or  instruments  for  setting  off  or 
r ■      .      "  •  .•         .'  •     .  -.'_.■  •    •         :    *    1  third,  !&•! 

•inch  approved  form,  coosi-  lo  360s, 

■ 
-  in  the 


kearhtgi  mast  Irst  be  marl 

tran-frmJ  to  the  re 
saamai  i.!-;-   t.     '!:-:•• 
aad  the  ac 


i  thence 
trumeuts  are  necessary. 


These  bteonveaieacr- 

i  tig  an 

'  t  angles,  is  made  in  one  iralM  bar.  a, 

ans  of  traverse  bars, 

•     f *och 

.Imit  the  str 

-■  6xed  by  th-  ral  transverse 

piece,  ».  which  is  screwed  to  the  t' 

■ad,  for  the  ere  of  a  radial  straigbt-edge,  r.  1. 

aad  clampiag  plate  are  pn.i  id-  .1  to  fix  the  radial  straight  bar, 

r.  at  an;  angle.    Immediately,  abw 

r,  aad  I  i  iif<.th  rod 

at  ltae.  aad  aaited  togeth-  i 
p.eve  embracing  the  socket,  l.  aad  adjasted  uw 


> ».  so  as  to  be  capable  of  being  kept  at  all  times  accu- 

..rjples  with  the  radiat  bar.  r.    At  a  short  distaaca 

Croat  the  ceatre  of  saotioa  of  the  radias  bar,  r,  is  a  segmental 

opening.  gra«l  .  .  an  each  side  of  the  i 

aad  for  the  minute  subdiviaion  of  the  graduations  of  the  quad- 
rant oa  the  piece,  x.  Br  this  apparatus  an;  angles  ma;  be 
measured  and  laid  off  b;  the  quadrant,  and  transferred  to  an; 
point  oa  the  paper  without  the  aid  of  an;  additional  instrument, 
as  the  whole  instrument  ma;  be  moved  to  an;  desired  point  on 
the  straight-edge,  r,  without  an;  shift  of  position  with  reference 
to  the  meridian  line  or  starting  point  With  additioaal  scales 
on  the  right  ancle  straight-edges,  j.  the  instrument  ma;  be  em- 
ployed, as  aa  offset  scale,  for  plotting  surer;*  aad  laving  down 


Oae  of  the  moat  economical!;  useful  instruments  of  the 
draughtsman  is  the  Pentagraph ;  but  it  is  one  which  requires 
such  extreme  accuracy  and  truthfulness  in  its  construction,  that 
its  consequent  cost  puts  it  out  of  the  reach  of  the  ma 
those  who  need  it.  B;  means  of  it,  drawings  may  be  copied  oa 
aa  enlarged  or  reduced  scale,  by  the  mere  action  of  carrying 
a  tracing  point  over  the  lines  of  the  original  drawing.  The 
motion  of  the  tracing  point  is  communicated  to  the  delineating 


pencil  b;  the  angular  movements  of  a  series  of  levers  osciPatiasT 
upon  a  I  -as  the 

,.  great. 


BOOK     OF     INDUSTRIAL     DESIGN. 


195 


required,  providing  for  the  increase  or  decrease  in  length  of  the 

two  radii,  but  in  such  a  manner  that  they  shall  continually 

be  in  the  same  proportion 

to  each  other.     This    is 

effected   by  making   the 

main    lever   with    joints 

midway  between  the  ex- 


Fig.  40. 


tremities  and  the 
centre  of  motion. 
It  is  necessary, 
however,  that  the  outer  joints  of  "---.       r-^^L 

the   lever   should   be   maintained  v    ^ - 

constantly  parallel  to  each  other, 

and  it  is  likewise  desirable  that  the  instrument  should  be  capa- 
ble of  adjustment  for  different  proportions,  otherwise  its  scope 
of  usefulness  would  be  sadly  narrowed.  These  several  condi- 
tions are  fulfilled  in  the  instrument  represented  in  our  engraving, 
fig.  40,  which  is  a  pentagraph  of  the  most  modern  and  approved 
design  and  construction.  The  main  lever,  a,  turns  upon  a  centre 
carried  by  the  weight,  b,  which  has  fine  points  upon  its  under 
side  to  prevent  its  slipping  upon  the  paper.  The  lever,  a, 
passes  through  a  socket  at  the  centre,  and  may  be  fixed  by  a 
pinching  screw  at  any  point  of  its  length ;  it  is  graduated  at  the 
side,  and  the  socket  is  formed  with  a  vernier  index  for  the  esti- 
mation of  minute  measurements.  To  the  extremities  of  the 
lever,  a,  are  jointed  the  discs,  c,  which  are  formed  with  sockets 
on  their  under  sides  to  receive  the  bars,  d,  e.  These  bars  are 
graduated  in  a  similar  manner  to  the  main  lever,  and  vernier 
indices  are  formed  in  the  plates,  c,  to  correspond.  The  paral- 
lelism of  these  bars  is  maintained  by  the  rods,  f  ;  the  tracing 
point  is  at  g,  and  the  delineating  pencil  at  h,  or  vice  versa,  as 
the  case  may  be.  A  string,  i,  is  passed  from  the  tracing  point 
through  guide  eyes  at  the  joints,  c,  c,  to  a  small  bell-crank  lever, 
at  n,  by  means  of  which  the  pencil  is  raised  when  it  is  not  wished 
to  mark ;  this  being  effected  by  drawing  the  string,  i,  at  the 
tracing  point.  As  represented  in  the  engraving,  the  instrument 
is  adjusted  to  copy  a  drawing  upon  an  enlarged  scale.  To 
obtain  the  correct  action  of  the  instrument  it  is  necessary  that 
the  tracer,  g,  pencil,  h,  and  centre  of  motion,  b,  be  in  a  straight 
line.  The  proportion  of  reduction  or  enlargement  being  deter- 
mined on,  the  main  lever,  a,  is  so  adjusted  in  its  socket,  b,  that 
the  portions  of  the  lever  on  each  side  of  the  centre  may  have 
this  proportion  to  each  other;  this  being  indicated  by  the 
graduated  scale  on  the  side  of  the  lever.  The  bars,  d,  e,  must 
then  be  correspondingly  adjusted  in  their  carrying  sockets,  the 


distance  between  the  tracer,  or  pencil,  and  joint  being  always 
ecmal  to  the  distance  between  the  joint  and  turning  centre  on 
the  respective  side  of  the  main  lever,  a.    The  instru- 
ment, when  adjusted,  is  balanced  on  its  centre  by 
means  of  the  sliding  weight,  j,  upon  the  lever,  a. 
In  some   pentagraphs   the   rods,  p,  are  dispensed 
with,  and  the  parallelism  of  the  bars,  d,  e,  main- 
tained by  a  belt,  k,  indicated  in 
dotted    lines,    passed    round   the 
peripheries  of  the  discs,  c,  grooved 
for   the   purpose. 
This  belt  is  usu- 
ally  of    thin  flat 
steel  wire,  similar 
to   that  used   for 
watch  springe — a 
belt   of    ordinary 
;<>-"  '  material    causing 

=■*' "  "■ —  inaccuracies  owing  to  its  elasticity.    The  arrange- 

ment in  which  the  rods  are  used  is,  however, 
superior,  as  the  belt  is  apt  to  slip,  or,  if  it  is  too  tight,  it  occa- 
sions an  injurious  strain  on  the  joints. 

Another  form  of  pentagraph  has  been  suggested  by  Mr.  R. 
Foster,  jun.,  of  Dublin,  which  seems  susceptible  of  being  rendered 
a  very  efficient  instrument.  It  is  delineated  in  fig.  41.  The 
small  and  shallow  circular  box,  a,  contains  the  actuating  mecha 
nism,  and  is  arranged  to  turn  at  pleasure  upon  the  fixed  centre 
stud,  b  ;  and  from  each  side  of  the  box,  a  rod,  t:,  d.  projects,  the 
points  of  the  rods  being  brought  into  a  horizontal  line  with  the 
Btud  centre,  b.     The  box  is  in  horizontal  section,  to  exhibit  the 

Fig.  «. 


internal  gearing.  The  end  of  each  rod  has  rack-teeth  upon  it, 
the  teeth  on  the  rod,  o,  gearing  with  a  spur-wheel,  e,  fas!  oil  a 
stud  in  the  centre  of  the  box  ;  whilst  the  other  rod.  d,  similarly 
gears,  with  a  pinion,  F;on  the  same  centre.  These  two  wheels 
are,  of  course,  changeable,  their  relative  radii  being  always 
determinable  by  the  proportion  to  be  observed  between  the 
original  and  the  copy,  of  any  drawing  to  be  reduced  or  enlarged 
by  the  instrument.  The  same  relation  is  also  to  be  kept  up 
between  the  lengths  of  the  two  rods,  in  order  that  hoth  the 
angular  and  longitudinal  traverse  actions  may  coincide.  It  is 
then  obvious  that  whatever  figure  is  traced  out  by  the  point 
on  one  rod,  will  be  delineated  by  the  pencil  on  the  other,  in 
the  proportion  determined  by  the  wheels  and  the  leverage  of 
tie  rods.  The  rods  may  be  either  worked  on  opposite  sides, 
or  both  on  the  same  side. 


Itt  Tlli 

In  •  put  the        :•  nt  in 

! 

:i    ill    the  « 

itniiiit  Bin. 

•  trustworthy  aids  in  the  prosecution  of  his  ttudiet 

D  t"  liifn  in  I 
Hi  ay  I-  nil — 

where  all  is  orderly  let  down." 

•nd  thai  itory  reroarl 

industrial  p  -  of  the 

i  •  u  Bmall  portion  of  the  which  wc  I  I 

presd  of  tliat  pari  ition  in  which 

•  far  behind. 
•■  M  tical  qualifii  •  nt  author  of  "  M 

entro.     On  the  right  side  an  the  men  <>f  fact--,  on  t ho 
-    t In-  men  "f  both."     Let  it  tx  i  to  weaken  this  disunion  of  : 

or uposite  class.     The  ri^lit  and  the  lift  may  each  hold  to, 

-,  but  nothing  really  g I  can  arise  fr"in  all  ihi>,  until  the  pra<  I 

upon  the  theoretical  desi|  n<  r,  which  the  hni«-r  will  niruiii  return,  in  op 
tpprehended  fact*  he  well,  "  is  the  parent,  not  the  proj 

-  in  practice  forma  jmrt  of  1 1 1 # -  prelude,  as  well  as  I 

by  judicious  theoretical  comp  <  I 

much  apart     "  The  dexterous  band  and  the  thoughtful  mind,"  the 
and  be  ■  h<  oath  e  brain.  Qnd  iln-ir  st 

foundry  it  may  l"-  designed,  or  however  clearly  it  may  l"-  w  ritten,  ran  make  n  draughtsman. 

i  ns,  the  ambitious  student  must  add  attentive  assiduity  and  patient  toil.     The  first 

■ih1  are  absolutely  essential.     Let  each  i  the  admirable  words  of 

'•  re  the  com n  level  has  received  two  education — tb< 

i  and  important,  from  himself."    Thi  Bacon  would  have 

In  In-  "Advice  on  the  Study  nnd  Practice  of tl  Wright  lias,  most  happily  and 

ilur  t'ipir.     II<  ■•lent  may  rest  assured  that,  without  industry,  and  u 

■   fame,  and  an  enthusiastic  desire  f"r  imp  ail  t"  inspire,  be  will  not 

cut;  and  bo  '■•it  thai  society  form-  a  very  different  opinion  of  the  man  of  sound  jui 

attempts,  anl  the  fanciful  and  vain,  who,  whilst  they  imagine  thi  i 
ii  than  othi  r  lives  in  indolent  or  trifling  pursuits,  without  acquiring  that  knowledge 

iracy  and  Buccess  in  practice."     These  are  the  wrll-considcrcd  ideas  of  men  who 
hi  and  action.     Their  pithy  eloquence  embodies  \\  hole  chapters  of  matter  \\  orthy  of 
ry,  where  thej  must   arouse  him  from  anj  dreamy  and  deceptive  contemplal 

rficial  thinker  is  bul  too  apl  t"  !"•  thus  led  awaj  j  that  such  compari- 

litions  which  h<-  perhaps  Bopercilioui 
i 

and  to  further  such  ei  written  tliis  book;  and  with  such  i  nowcommH 


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